Prefix-Free Regular-Expression Matching

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Prefix-Free Regular-Expression Matching"

Transcription

1 Prefix-Free Regulr-Expression Mthing Yo-Su Hn, Yjun Wng nd Derik Wood Deprtment of Computer Siene HKUST Prefix-Free Regulr-Expression Mthing p.1/15

2 Pttern Mthing Given pttern P nd text T, find ll sustrings of T tht re in P. P = 1: string pttern mthing [BM, KMP] P = k: keyword pttern mthing [AC] P is regulr expression: regulr-expression pttern mthing!!! Prefix-Free Regulr-Expression Mthing p.2/15

3 Overview Bsi Notions Relted Work Regulr-Expression Mthing Infix-Free Regulr-Expression Mthing Prefix-Free Regulr-Expression Mthing Determine whether or not L(E) is prefix-free Conlusions Prefix-Free Regulr-Expression Mthing p.3/15

4 Bsi Notions An utomton A is speified y tuple (Q, Σ,δ,s,F); Q finite set of sttes Σ finite lphet δ Q Σ Q s Q strt stte F Q set of finl sttes λ = the null-string symol A = Q + δ E = the numer of hrter ppernes in given regulr expression E Prefix-Free Regulr-Expression Mthing p.4/15

5 Bsi Notions Given trnsition (p,,q) in δ p hs n out-trnsition q hs n in-trnsition p is soure stte of q q is trget stte of p A to e non-returning if the strt stte of A does not hve ny in-trnsitions A to e non-exiting if finl stte of A does not hve ny out-trnsitions p q Prefix-Free Regulr-Expression Mthing p.4/15

6 Bsi Notions Given two strings x nd y over Σ, we sy x is prefix of y if there exists z Σ suh tht xz = y. x is n infix of y if there exists u,v Σ suh tht uxv = y; we often ll x sustring of y. Prefix-Free Regulr-Expression Mthing p.4/15

7 Bsi Notions We define lnguge L to e prefix-free if no string in L is prefix of ny other strings in L. infix-free if no string in L is n infix of ny other strings in L. Prefix-Free Regulr-Expression Mthing p.4/15

8 Relted Work Given regulr expression E nd text T, The memership prolem: We n determine whether or not T L(E) in O(mn) time [Thompson] The deision prolem: We n determine whether or not there is sustring of T tht is in L(E)) in O(mn) time [Aho] or in O(m log n) time [Myers] The reognition prolem: We n report ll end positions of mthing sustrings of T in O(mn) time [Aho] or in O(m log n) time [Myers] The identifition prolem: We n report ll (strt, end) positions of mthing sustrings of T in O(mn log n) time [Myers et l.] Prefix-Free Regulr-Expression Mthing p.5/15

9 The Memership Prolem E = ( + ) nd T = Prefix-Free Regulr-Expression Mthing p.6/15

10 The Memership Prolem E = ( + ) nd T = Prefix-Free Regulr-Expression Mthing p.6/15

11 The Memership Prolem E = ( + ) nd T = Prefix-Free Regulr-Expression Mthing p.6/15

12 The Memership Prolem E = ( + ) nd T = Prefix-Free Regulr-Expression Mthing p.6/15

13 The Memership Prolem E = ( + ) nd T = Prefix-Free Regulr-Expression Mthing p.6/15

14 The Memership Prolem E = ( + ) nd T = Prefix-Free Regulr-Expression Mthing p.6/15

15 The Memership Prolem E = ( + ) nd T = Prefix-Free Regulr-Expression Mthing p.6/15

16 The Memership Prolem E = ( + ) nd T = Prefix-Free Regulr-Expression Mthing p.6/15

17 The Memership Prolem E = ( + ) nd T = Prefix-Free Regulr-Expression Mthing p.6/15

18 The Memership Prolem E = ( + ) nd T = Prefix-Free Regulr-Expression Mthing p.6/15

19 The Reognition Prolem Given E over Σ, we prepend Σ to E; thus, llowing mthing to egin t ny position in T. Σ ( + ) Σ Prefix-Free Regulr-Expression Mthing p.7/15

20 The Reognition Prolem Given E over Σ, we prepend Σ to E; thus, llowing mthing to egin t ny position in T. ExpressionMthing (A, T) Q = null({s}) if f Q then output λ for j=1 to n Q = null(goto(q,w j )) if f Q then output j null(q) omputes ll sttes in A tht n e rehed from stte in the set Q of sttes y null trnsitions goto(q,w j ) gives ll sttes tht n e rehed from stte in Q y trnsition with w j, the urrent input hrter Prefix-Free Regulr-Expression Mthing p.7/15

21 The Reognition Prolem Given E over Σ, we prepend Σ to E; thus, llowing mthing to egin t ny position in T. E = ( + ) T Given regulr expression E nd text T, we n find ll end positions of mthing sustrings of T in O(mn) worst-se time using O(m) spe [Crohemore nd Hnrt]. Prefix-Free Regulr-Expression Mthing p.7/15

22 The Identifition Prolem Given regulr expression E nd text T, we n identify ll mthing sustrings of T tht elong to L(E) in O(mn 2 ) worst-se time using O(m) spe. Note tht the lgorithm of Myers et l. tkes O(mn log n) time using O(m log n) spe. Prefix-Free Regulr-Expression Mthing p.8/15

23 Infix-Free Regulr-Expression Mthing L IN L PRE L REG T Given n infix-free regulr expression E nd text T, we n identify ll mthing sustrings of T tht elong to L(E) in O(mn) worst-se time using O(m) spe. Prefix-Free Regulr-Expression Mthing p.9/15

24 Prefix-Free Regulr-Expression Mthing L IN L PRE L REG If E is infix-free, we hve n O(mn) running time lgorithm If E is (norml) regulr expression, we hve n O(mn 2 ) running time lgorithm If E is prefix-free, there re t most n mthing sustrings of T tht elong to L(E), where n is the size of T Prefix-Free Regulr-Expression Mthing p.10/15

25 Prefix-Free Regulr-Expression Mthing Given prefix-free regulr expression E nd text T, we find ll end positions of mthing sustrings of T in O(mn) time. T Let P = {p 1,p 2,...,p k } e the set of end positions of mthing sustrings for k n Construt the Thompson utomton A = (Q, Σ,δ,s,f ) for E R Sn T R = w n w 1 strting from the lst position p k in P to find the orresponding strt position Prefix-Free Regulr-Expression Mthing p.10/15

26 Prefix-Free Regulr-Expression Mthing T Q 15 For urrent input position i in T R, Q 15 is set of sttes suh tht there is pth from s to eh stte in Q 15 tht spells out w 15 w 14 w i. We keep reding T R until we meet f. Prefix-Free Regulr-Expression Mthing p.10/15

27 Prefix-Free Regulr-Expression Mthing T Q 13 Q 15 Prefix-Free Regulr-Expression Mthing p.10/15

28 Prefix-Free Regulr-Expression Mthing T Q 10 Q 13 Q 15 Prefix-Free Regulr-Expression Mthing p.10/15

29 Prefix-Free Regulr-Expression Mthing T Q 9 Q 10 Q 13 Q 15 In the worst-se, there re k suh sets of sttes nd we need O(km) time for eh hrter of T to updte these k sets. Thus, the totl running time is O(mn 2 ) in the worst-se sine k is t most n. Prefix-Free Regulr-Expression Mthing p.10/15

30 Prefix-Free Regulr-Expression Mthing If stte r in A is rehed from two different sttes p nd q, where p Q i nd q Q j, when reding hrter w h in EM, where h i < j, then oth pths from p nd q vi r nnot reh f y reding ny prefix of the remining input in EM. p Q i, q Q j T R j i h Q i Q j p r q Prefix-Free Regulr-Expression Mthing p.11/15

31 Prefix-Free Regulr-Expression Mthing If stte r in A is rehed from two different sttes p nd q, where p Q i nd q Q j, when reding hrter w h in EM, where h i < j, then oth pths from p nd q vi r nnot reh f y reding ny prefix of the remining input in EM. Eh stte in A ppers in t most one rehle set Any two sets of rehle sttes re disjoint We need t most O(m) time to updte ll sets of rehle sttes simultneously t eh step Given prefix-free regulr expression E nd text T, we n identify ll mthing sustrings of T tht elong to L(E) in O(mn) worst-se time using O(m) spe. Prefix-Free Regulr-Expression Mthing p.11/15

32 Prefix-Freeness An FA A is prefix-free if L(A) is prefix-free A DFA A is prefix-free if it is non-exiting Wht out the NFA se? Prefix-Free Regulr-Expression Mthing p.12/15

33 Prefix-Freeness An FA A is prefix-free if L(A) is prefix-free A DFA A is prefix-free if it is non-exiting Wht out the NFA se? If n NFA A is prefix-free, then A must e non-exiting However, the reverse does not hold Prefix-Free Regulr-Expression Mthing p.12/15

34 Prefix-Freeness An FA A is prefix-free if L(A) is prefix-free A DFA A is prefix-free if it is non-exiting Wht out the NFA se? If n NFA A is prefix-free, then A must e non-exiting However, the reverse does not hold s f Prefix-Free Regulr-Expression Mthing p.12/15

35 Stte-Pir Grph Given finite-stte utomton A = (Q, Σ, δ, s, f), we define the stte-pir grph G A = (V,E), where V is set of nodes nd E is set of edges, s follows: V = {(i,j) q i nd q j Q} nd E = {((i,j),, (x,y)) (q i,,q x ) nd (q j,,q y ) δ nd Σ} ,2 1,1 3,3 4,6 4,4 5,5 6,6 5,7 7,7 Prefix-Free Regulr-Expression Mthing p.13/15

36 Stte-Pir Grph & Prefix-Freeness CPM 2005 Given finite-stte utomton A, L(A) is prefix-free if nd only if there is no pth from (1, 1) to (m,j), for ny j m, in G A ,2 1,1 3,3 4,6 4,4 5,5 6,6 5,7 7,7 Prefix-Free Regulr-Expression Mthing p.14/15

37 Stte-Pir Grph & Prefix-Freeness CPM 2005 Given finite-stte utomton A, L(A) is prefix-free if nd only if there is no pth from (1, 1) to (m,j), for ny j m, in G A Given finite-stte utomton A = (Q, Σ, δ, s, f), we n determine whether or not L(A) is prefix-free in O( Q 2 + δ 2 ) worst-se time Let G A = (V, E) e the stte-pir grph of A V = Q 2 Let δ i denote the set of out-trnsitions from stte q i in A δ = m i=1 δ i, where m = Q node (i, j) in G A n hve t most δ i δ j out-trnsitions E = m i,j=1 δ i δ j δ 2 Prefix-Free Regulr-Expression Mthing p.14/15

38 Stte-Pir Grph & Prefix-Freeness CPM 2005 Given finite-stte utomton A, L(A) is prefix-free if nd only if there is no pth from (1, 1) to (m,j), for ny j m, in G A Given finite-stte utomton A = (Q, Σ, δ, s, f), we n determine whether or not L(A) is prefix-free in O( Q 2 + δ 2 ) worst-se time Given regulr expression E, we n determine whether or not L(E) is prefix-free in O( E 2 ) worst-se time Construt the Thompson utomton for E Q = δ = O( E ) Prefix-Free Regulr-Expression Mthing p.14/15

39 Conlusions Solve the prefix-free regulr-expression mthing prolem in O(mn) time using O(m) spe sed on the Thompson utomt Determine whether or not L(A) is prefix-free for given NFA A in polynomil time sed on stte-pir grphs Prefix-Free Regulr-Expression Mthing p.15/15

Regular Languages and Applications

Regular Languages and Applications Regulr Lnguges nd Applictions Yo-Su Hn Deprtment of Computer Science Yonsei University 1-1 SNU 4/14 Regulr Lnguges An old nd well-known topic in CS Kleene Theorem in 1959 FA (finite-stte utomton) constructions:

More information

Data Structures and Algorithm. Xiaoqing Zheng

Data Structures and Algorithm. Xiaoqing Zheng Dt Strutures nd Algorithm Xioqing Zheng zhengxq@fudn.edu.n String mthing prolem Pttern P ours with shift s in text T (or, equivlently, tht pttern P ours eginning t position s + in text T) if T[s +... s

More information

Regular languages refresher

Regular languages refresher Regulr lnguges refresher 1 Regulr lnguges refresher Forml lnguges Alphet = finite set of letters Word = sequene of letter Lnguge = set of words Regulr lnguges defined equivlently y Regulr expressions Finite-stte

More information

CS311 Computational Structures Regular Languages and Regular Grammars. Lecture 6

CS311 Computational Structures Regular Languages and Regular Grammars. Lecture 6 CS311 Computtionl Strutures Regulr Lnguges nd Regulr Grmmrs Leture 6 1 Wht we know so fr: RLs re losed under produt, union nd * Every RL n e written s RE, nd every RE represents RL Every RL n e reognized

More information

Nondeterministic Automata vs Deterministic Automata

Nondeterministic Automata vs Deterministic Automata Nondeterministi Automt vs Deterministi Automt We lerned tht NFA is onvenient model for showing the reltionships mong regulr grmmrs, FA, nd regulr expressions, nd designing them. However, we know tht n

More information

Chapter Five: Nondeterministic Finite Automata. Formal Language, chapter 5, slide 1

Chapter Five: Nondeterministic Finite Automata. Formal Language, chapter 5, slide 1 Chpter Five: Nondeterministic Finite Automt Forml Lnguge, chpter 5, slide 1 1 A DFA hs exctly one trnsition from every stte on every symol in the lphet. By relxing this requirement we get relted ut more

More information

Running an NFA & the subset algorithm (NFA->DFA) CS 350 Fall 2018 gilray.org/classes/fall2018/cs350/

Running an NFA & the subset algorithm (NFA->DFA) CS 350 Fall 2018 gilray.org/classes/fall2018/cs350/ Running n NFA & the suset lgorithm (NFA->DFA) CS 350 Fll 2018 gilry.org/lsses/fll2018/s350/ 1 NFAs operte y simultneously exploring ll pths nd epting if ny pth termintes t n ept stte.!2 Try n exmple: L

More information

Finite State Automata and Determinisation

Finite State Automata and Determinisation Finite Stte Automt nd Deterministion Tim Dworn Jnury, 2016 Lnguges fs nf re df Deterministion 2 Outline 1 Lnguges 2 Finite Stte Automt (fs) 3 Non-deterministi Finite Stte Automt (nf) 4 Regulr Expressions

More information

Formal Languages and Automata

Formal Languages and Automata Moile Computing nd Softwre Engineering p. 1/5 Forml Lnguges nd Automt Chpter 2 Finite Automt Chun-Ming Liu cmliu@csie.ntut.edu.tw Deprtment of Computer Science nd Informtion Engineering Ntionl Tipei University

More information

AUTOMATA AND LANGUAGES. Definition 1.5: Finite Automaton

AUTOMATA AND LANGUAGES. Definition 1.5: Finite Automaton 25. Finite Automt AUTOMATA AND LANGUAGES A system of computtion tht only hs finite numer of possile sttes cn e modeled using finite utomton A finite utomton is often illustrted s stte digrm d d d. d q

More information

Nondeterminism and Nodeterministic Automata

Nondeterminism and Nodeterministic Automata Nondeterminism nd Nodeterministic Automt 61 Nondeterminism nd Nondeterministic Automt The computtionl mchine models tht we lerned in the clss re deterministic in the sense tht the next move is uniquely

More information

Minimal DFA. minimal DFA for L starting from any other

Minimal DFA. minimal DFA for L starting from any other Miniml DFA Among the mny DFAs ccepting the sme regulr lnguge L, there is exctly one (up to renming of sttes) which hs the smllest possile numer of sttes. Moreover, it is possile to otin tht miniml DFA

More information

Deterministic Finite Automata

Deterministic Finite Automata Finite Automt Deterministic Finite Automt H. Geuvers nd J. Rot Institute for Computing nd Informtion Sciences Version: fll 2016 J. Rot Version: fll 2016 Tlen en Automten 1 / 21 Outline Finite Automt Finite

More information

CHAPTER 1 Regular Languages. Contents. definitions, examples, designing, regular operations. Non-deterministic Finite Automata (NFA)

CHAPTER 1 Regular Languages. Contents. definitions, examples, designing, regular operations. Non-deterministic Finite Automata (NFA) Finite Automt (FA or DFA) CHAPTER Regulr Lnguges Contents definitions, exmples, designing, regulr opertions Non-deterministic Finite Automt (NFA) definitions, equivlence of NFAs DFAs, closure under regulr

More information

Theory of Computation Regular Languages

Theory of Computation Regular Languages Theory of Computtion Regulr Lnguges Bow-Yw Wng Acdemi Sinic Spring 2012 Bow-Yw Wng (Acdemi Sinic) Regulr Lnguges Spring 2012 1 / 38 Schemtic of Finite Automt control 0 0 1 0 1 1 1 0 Figure: Schemtic of

More information

Nondeterministic Finite Automata

Nondeterministic Finite Automata Nondeterministi Finite utomt The Power of Guessing Tuesdy, Otoer 4, 2 Reding: Sipser.2 (first prt); Stoughton 3.3 3.5 S235 Lnguges nd utomt eprtment of omputer Siene Wellesley ollege Finite utomton (F)

More information

Homework 3 Solutions

Homework 3 Solutions CS 341: Foundtions of Computer Science II Prof. Mrvin Nkym Homework 3 Solutions 1. Give NFAs with the specified numer of sttes recognizing ech of the following lnguges. In ll cses, the lphet is Σ = {,1}.

More information

DFA Minimization and Applications

DFA Minimization and Applications DFA Minimiztion nd Applictions Mondy, Octoer 15, 2007 Reding: toughton 3.12 C235 Lnguges nd Automt Deprtment of Computer cience Wellesley College Gols for ody o Answer ny P3 questions you might hve. o

More information

Regular expressions, Finite Automata, transition graphs are all the same!!

Regular expressions, Finite Automata, transition graphs are all the same!! CSI 3104 /Winter 2011: Introduction to Forml Lnguges Chpter 7: Kleene s Theorem Chpter 7: Kleene s Theorem Regulr expressions, Finite Automt, trnsition grphs re ll the sme!! Dr. Neji Zgui CSI3104-W11 1

More information

Let's start with an example:

Let's start with an example: Finite Automt Let's strt with n exmple: Here you see leled circles tht re sttes, nd leled rrows tht re trnsitions. One of the sttes is mrked "strt". One of the sttes hs doule circle; this is terminl stte

More information

Theory of Computation Regular Languages. (NTU EE) Regular Languages Fall / 38

Theory of Computation Regular Languages. (NTU EE) Regular Languages Fall / 38 Theory of Computtion Regulr Lnguges (NTU EE) Regulr Lnguges Fll 2017 1 / 38 Schemtic of Finite Automt control 0 0 1 0 1 1 1 0 Figure: Schemtic of Finite Automt A finite utomton hs finite set of control

More information

First Midterm Examination

First Midterm Examination 24-25 Fll Semester First Midterm Exmintion ) Give the stte digrm of DFA tht recognizes the lnguge A over lphet Σ = {, } where A = {w w contins or } 2) The following DFA recognizes the lnguge B over lphet

More information

1. For each of the following theorems, give a two or three sentence sketch of how the proof goes or why it is not true.

1. For each of the following theorems, give a two or three sentence sketch of how the proof goes or why it is not true. York University CSE 2 Unit 3. DFA Clsses Converting etween DFA, NFA, Regulr Expressions, nd Extended Regulr Expressions Instructor: Jeff Edmonds Don t chet y looking t these nswers premturely.. For ech

More information

Lecture 08: Feb. 08, 2019

Lecture 08: Feb. 08, 2019 4CS4-6:Theory of Computtion(Closure on Reg. Lngs., regex to NDFA, DFA to regex) Prof. K.R. Chowdhry Lecture 08: Fe. 08, 2019 : Professor of CS Disclimer: These notes hve not een sujected to the usul scrutiny

More information

= state, a = reading and q j

= state, a = reading and q j 4 Finite Automt CHAPTER 2 Finite Automt (FA) (i) Derterministi Finite Automt (DFA) A DFA, M Q, q,, F, Where, Q = set of sttes (finite) q Q = the strt/initil stte = input lphet (finite) (use only those

More information

Worked out examples Finite Automata

Worked out examples Finite Automata Worked out exmples Finite Automt Exmple Design Finite Stte Automton which reds inry string nd ccepts only those tht end with. Since we re in the topic of Non Deterministic Finite Automt (NFA), we will

More information

Java II Finite Automata I

Java II Finite Automata I Jv II Finite Automt I Bernd Kiefer Bernd.Kiefer@dfki.de Deutsches Forschungszentrum für künstliche Intelligenz Finite Automt I p.1/13 Processing Regulr Expressions We lredy lerned out Jv s regulr expression

More information

CSCI 340: Computational Models. Transition Graphs. Department of Computer Science

CSCI 340: Computational Models. Transition Graphs. Department of Computer Science CSCI 340: Computtionl Models Trnsition Grphs Chpter 6 Deprtment of Computer Science Relxing Restrints on Inputs We cn uild n FA tht ccepts only the word! 5 sttes ecuse n FA cn only process one letter t

More information

Technische Universität München Winter term 2009/10 I7 Prof. J. Esparza / J. Křetínský / M. Luttenberger 11. Februar Solution

Technische Universität München Winter term 2009/10 I7 Prof. J. Esparza / J. Křetínský / M. Luttenberger 11. Februar Solution Tehnishe Universität Münhen Winter term 29/ I7 Prof. J. Esprz / J. Křetínský / M. Luttenerger. Ferur 2 Solution Automt nd Forml Lnguges Homework 2 Due 5..29. Exerise 2. Let A e the following finite utomton:

More information

CS375: Logic and Theory of Computing

CS375: Logic and Theory of Computing CS375: Logic nd Theory of Computing Fuhu (Frnk) Cheng Deprtment of Computer Science University of Kentucky 1 Tle of Contents: Week 1: Preliminries (set lger, reltions, functions) (red Chpters 1-4) Weeks

More information

CS 301. Lecture 04 Regular Expressions. Stephen Checkoway. January 29, 2018

CS 301. Lecture 04 Regular Expressions. Stephen Checkoway. January 29, 2018 CS 301 Lecture 04 Regulr Expressions Stephen Checkowy Jnury 29, 2018 1 / 35 Review from lst time NFA N = (Q, Σ, δ, q 0, F ) where δ Q Σ P (Q) mps stte nd n lphet symol (or ) to set of sttes We run n NFA

More information

Grammar. Languages. Content 5/10/16. Automata and Languages. Regular Languages. Regular Languages

Grammar. Languages. Content 5/10/16. Automata and Languages. Regular Languages. Regular Languages 5//6 Grmmr Automt nd Lnguges Regulr Grmmr Context-free Grmmr Context-sensitive Grmmr Prof. Mohmed Hmd Softwre Engineering L. The University of Aizu Jpn Regulr Lnguges Context Free Lnguges Context Sensitive

More information

1.4 Nonregular Languages

1.4 Nonregular Languages 74 1.4 Nonregulr Lnguges The number of forml lnguges over ny lphbet (= decision/recognition problems) is uncountble On the other hnd, the number of regulr expressions (= strings) is countble Hence, ll

More information

First Midterm Examination

First Midterm Examination Çnky University Deprtment of Computer Engineering 203-204 Fll Semester First Midterm Exmintion ) Design DFA for ll strings over the lphet Σ = {,, c} in which there is no, no nd no cc. 2) Wht lnguge does

More information

CS 573 Automata Theory and Formal Languages

CS 573 Automata Theory and Formal Languages Non-determinism Automt Theory nd Forml Lnguges Professor Leslie Lnder Leture # 3 Septemer 6, 2 To hieve our gol, we need the onept of Non-deterministi Finite Automton with -moves (NFA) An NFA is tuple

More information

Designing finite automata II

Designing finite automata II Designing finite utomt II Prolem: Design DFA A such tht L(A) consists of ll strings of nd which re of length 3n, for n = 0, 1, 2, (1) Determine wht to rememer out the input string Assign stte to ech of

More information

Languages & Automata

Languages & Automata Lnguges & Automt Dr. Lim Nughton Lnguges A lnguge is sed on n lphet which is finite set of smols such s {, } or {, } or {,..., z}. If Σ is n lphet, string over Σ is finite sequence of letters from Σ, (strings

More information

Chapter 1, Part 1. Regular Languages. CSC527, Chapter 1, Part 1 c 2012 Mitsunori Ogihara 1

Chapter 1, Part 1. Regular Languages. CSC527, Chapter 1, Part 1 c 2012 Mitsunori Ogihara 1 Chpter 1, Prt 1 Regulr Lnguges CSC527, Chpter 1, Prt 1 c 2012 Mitsunori Ogihr 1 Finite Automt A finite utomton is system for processing ny finite sequence of symols, where the symols re chosen from finite

More information

Finite-State Automata: Recap

Finite-State Automata: Recap Finite-Stte Automt: Recp Deepk D Souz Deprtment of Computer Science nd Automtion Indin Institute of Science, Bnglore. 09 August 2016 Outline 1 Introduction 2 Forml Definitions nd Nottion 3 Closure under

More information

The University of Nottingham SCHOOL OF COMPUTER SCIENCE A LEVEL 2 MODULE, SPRING SEMESTER MACHINES AND THEIR LANGUAGES ANSWERS

The University of Nottingham SCHOOL OF COMPUTER SCIENCE A LEVEL 2 MODULE, SPRING SEMESTER MACHINES AND THEIR LANGUAGES ANSWERS The University of ottinghm SCHOOL OF COMPUTR SCIC A LVL 2 MODUL, SPRIG SMSTR 2015 2016 MACHIS AD THIR LAGUAGS ASWRS Time llowed TWO hours Cndidtes my omplete the front over of their nswer ook nd sign their

More information

GNFA GNFA GNFA GNFA GNFA

GNFA GNFA GNFA GNFA GNFA DFA RE NFA DFA -NFA REX GNFA Definition GNFA A generlize noneterministic finite utomton (GNFA) is grph whose eges re lele y regulr expressions, with unique strt stte with in-egree, n unique finl stte with

More information

CS415 Compilers. Lexical Analysis and. These slides are based on slides copyrighted by Keith Cooper, Ken Kennedy & Linda Torczon at Rice University

CS415 Compilers. Lexical Analysis and. These slides are based on slides copyrighted by Keith Cooper, Ken Kennedy & Linda Torczon at Rice University CS415 Compilers Lexicl Anlysis nd These slides re sed on slides copyrighted y Keith Cooper, Ken Kennedy & Lind Torczon t Rice University First Progrmming Project Instruction Scheduling Project hs een posted

More information

NON-DETERMINISTIC FSA

NON-DETERMINISTIC FSA Tw o types of non-determinism: NON-DETERMINISTIC FS () Multiple strt-sttes; strt-sttes S Q. The lnguge L(M) ={x:x tkes M from some strt-stte to some finl-stte nd ll of x is proessed}. The string x = is

More information

Chapter 4 Regular Grammar and Regular Sets. (Solutions / Hints)

Chapter 4 Regular Grammar and Regular Sets. (Solutions / Hints) C K Ngpl Forml Lnguges nd utomt Theory Chpter 4 Regulr Grmmr nd Regulr ets (olutions / Hints) ol. (),,,,,,,,,,,,,,,,,,,,,,,,,, (),, (c) c c, c c, c, c, c c, c, c, c, c, c, c, c c,c, c, c, c, c, c, c, c,

More information

CISC 4090 Theory of Computation

CISC 4090 Theory of Computation 9/6/28 Stereotypicl computer CISC 49 Theory of Computtion Finite stte mchines & Regulr lnguges Professor Dniel Leeds dleeds@fordhm.edu JMH 332 Centrl processing unit (CPU) performs ll the instructions

More information

Lecture 6 Regular Grammars

Lecture 6 Regular Grammars Lecture 6 Regulr Grmmrs COT 4420 Theory of Computtion Section 3.3 Grmmr A grmmr G is defined s qudruple G = (V, T, S, P) V is finite set of vribles T is finite set of terminl symbols S V is specil vrible

More information

a,b a 1 a 2 a 3 a,b 1 a,b a,b 2 3 a,b a,b a 2 a,b CS Determinisitic Finite Automata 1

a,b a 1 a 2 a 3 a,b 1 a,b a,b 2 3 a,b a,b a 2 a,b CS Determinisitic Finite Automata 1 CS4 45- Determinisitic Finite Automt -: Genertors vs. Checkers Regulr expressions re one wy to specify forml lnguge String Genertor Genertes strings in the lnguge Deterministic Finite Automt (DFA) re nother

More information

CHAPTER 1 Regular Languages. Contents

CHAPTER 1 Regular Languages. Contents Finite Automt (FA or DFA) CHAPTE 1 egulr Lnguges Contents definitions, exmples, designing, regulr opertions Non-deterministic Finite Automt (NFA) definitions, euivlence of NFAs nd DFAs, closure under regulr

More information

Table of contents: Lecture N Summary... 3 What does automata mean?... 3 Introduction to languages... 3 Alphabets... 3 Strings...

Table of contents: Lecture N Summary... 3 What does automata mean?... 3 Introduction to languages... 3 Alphabets... 3 Strings... Tle of contents: Lecture N0.... 3 ummry... 3 Wht does utomt men?... 3 Introduction to lnguges... 3 Alphets... 3 trings... 3 Defining Lnguges... 4 Lecture N0. 2... 7 ummry... 7 Kleene tr Closure... 7 Recursive

More information

State Complexity of Union and Intersection of Binary Suffix-Free Languages

State Complexity of Union and Intersection of Binary Suffix-Free Languages Stte Complexity of Union nd Intersetion of Binry Suffix-Free Lnguges Glin Jirásková nd Pvol Olejár Slovk Ademy of Sienes nd Šfárik University, Košie 0000 1111 0000 1111 Glin Jirásková nd Pvol Olejár Binry

More information

CSCI 340: Computational Models. Kleene s Theorem. Department of Computer Science

CSCI 340: Computational Models. Kleene s Theorem. Department of Computer Science CSCI 340: Computtionl Models Kleene s Theorem Chpter 7 Deprtment of Computer Science Unifiction In 1954, Kleene presented (nd proved) theorem which (in our version) sttes tht if lnguge cn e defined y ny

More information

Some Theory of Computation Exercises Week 1

Some Theory of Computation Exercises Week 1 Some Theory of Computtion Exercises Week 1 Section 1 Deterministic Finite Automt Question 1.3 d d d d u q 1 q 2 q 3 q 4 q 5 d u u u u Question 1.4 Prt c - {w w hs even s nd one or two s} First we sk whether

More information

CSC 311 Theory of Computation

CSC 311 Theory of Computation CSC 11 Theory of Computtion Tutoril on DFAs, NFAs, regulr expressions, regulr grmmr, closure of regulr lnguges, context-free grmmrs, non-deterministic push-down utomt, Turing mchines,etc. Tutoril 2 Second

More information

CS 310 (sec 20) - Winter Final Exam (solutions) SOLUTIONS

CS 310 (sec 20) - Winter Final Exam (solutions) SOLUTIONS CS 310 (sec 20) - Winter 2003 - Finl Exm (solutions) SOLUTIONS 1. (Logic) Use truth tles to prove the following logicl equivlences: () p q (p p) (q q) () p q (p q) (p q) () p q p q p p q q (q q) (p p)

More information

Kleene s Theorem. Kleene s Theorem. Kleene s Theorem. Kleene s Theorem. Kleene s Theorem. Kleene s Theorem 2/16/15

Kleene s Theorem. Kleene s Theorem. Kleene s Theorem. Kleene s Theorem. Kleene s Theorem. Kleene s Theorem 2/16/15 Models of Comput:on Lecture #8 Chpter 7 con:nued Any lnguge tht e defined y regulr expression, finite utomton, or trnsi:on grph cn e defined y ll three methods We prove this y showing tht ny lnguge defined

More information

CMPSCI 250: Introduction to Computation. Lecture #31: What DFA s Can and Can t Do David Mix Barrington 9 April 2014

CMPSCI 250: Introduction to Computation. Lecture #31: What DFA s Can and Can t Do David Mix Barrington 9 April 2014 CMPSCI 250: Introduction to Computtion Lecture #31: Wht DFA s Cn nd Cn t Do Dvid Mix Brrington 9 April 2014 Wht DFA s Cn nd Cn t Do Deterministic Finite Automt Forml Definition of DFA s Exmples of DFA

More information

Nondeterminism. Nondeterministic Finite Automata. Example: Moves on a Chessboard. Nondeterminism (2) Example: Chessboard (2) Formal NFA

Nondeterminism. Nondeterministic Finite Automata. Example: Moves on a Chessboard. Nondeterminism (2) Example: Chessboard (2) Formal NFA Nondeterminism Nondeterministic Finite Automt Nondeterminism Subset Construction A nondeterministic finite utomton hs the bility to be in severl sttes t once. Trnsitions from stte on n input symbol cn

More information

Global alignment. Genome Rearrangements Finding preserved genes. Lecture 18

Global alignment. Genome Rearrangements Finding preserved genes. Lecture 18 Computt onl Biology Leture 18 Genome Rerrngements Finding preserved genes We hve seen before how to rerrnge genome to obtin nother one bsed on: Reversls Knowledge of preserved bloks (or genes) Now we re

More information

CS 373, Spring Solutions to Mock midterm 1 (Based on first midterm in CS 273, Fall 2008.)

CS 373, Spring Solutions to Mock midterm 1 (Based on first midterm in CS 273, Fall 2008.) CS 373, Spring 29. Solutions to Mock midterm (sed on first midterm in CS 273, Fll 28.) Prolem : Short nswer (8 points) The nswers to these prolems should e short nd not complicted. () If n NF M ccepts

More information

80 CHAPTER 2. DFA S, NFA S, REGULAR LANGUAGES. 2.6 Finite State Automata With Output: Transducers

80 CHAPTER 2. DFA S, NFA S, REGULAR LANGUAGES. 2.6 Finite State Automata With Output: Transducers 80 CHAPTER 2. DFA S, NFA S, REGULAR LANGUAGES 2.6 Finite Stte Automt With Output: Trnsducers So fr, we hve only considered utomt tht recognize lnguges, i.e., utomt tht do not produce ny output on ny input

More information

Assignment 1 Automata, Languages, and Computability. 1 Finite State Automata and Regular Languages

Assignment 1 Automata, Languages, and Computability. 1 Finite State Automata and Regular Languages Deprtment of Computer Science, Austrlin Ntionl University COMP2600 Forml Methods for Softwre Engineering Semester 2, 206 Assignment Automt, Lnguges, nd Computility Smple Solutions Finite Stte Automt nd

More information

Thoery of Automata CS402

Thoery of Automata CS402 Thoery of Automt C402 Theory of Automt Tle of contents: Lecture N0. 1... 4 ummry... 4 Wht does utomt men?... 4 Introduction to lnguges... 4 Alphets... 4 trings... 4 Defining Lnguges... 5 Lecture N0. 2...

More information

Harvard University Computer Science 121 Midterm October 23, 2012

Harvard University Computer Science 121 Midterm October 23, 2012 Hrvrd University Computer Science 121 Midterm Octoer 23, 2012 This is closed-ook exmintion. You my use ny result from lecture, Sipser, prolem sets, or section, s long s you quote it clerly. The lphet is

More information

Non Deterministic Automata. Linz: Nondeterministic Finite Accepters, page 51

Non Deterministic Automata. Linz: Nondeterministic Finite Accepters, page 51 Non Deterministic Automt Linz: Nondeterministic Finite Accepters, pge 51 1 Nondeterministic Finite Accepter (NFA) Alphbet ={} q 1 q2 q 0 q 3 2 Nondeterministic Finite Accepter (NFA) Alphbet ={} Two choices

More information

1 Nondeterministic Finite Automata

1 Nondeterministic Finite Automata 1 Nondeterministic Finite Automt Suppose in life, whenever you hd choice, you could try oth possiilities nd live your life. At the end, you would go ck nd choose the one tht worked out the est. Then you

More information

1 From NFA to regular expression

1 From NFA to regular expression Note 1: How to convert DFA/NFA to regulr expression Version: 1.0 S/EE 374, Fll 2017 Septemer 11, 2017 In this note, we show tht ny DFA cn e converted into regulr expression. Our construction would work

More information

12.1 Nondeterminism Nondeterministic Finite Automata. a a b ε. CS125 Lecture 12 Fall 2014

12.1 Nondeterminism Nondeterministic Finite Automata. a a b ε. CS125 Lecture 12 Fall 2014 CS125 Lecture 12 Fll 2014 12.1 Nondeterminism The ide of nondeterministic computtions is to llow our lgorithms to mke guesses, nd only require tht they ccept when the guesses re correct. For exmple, simple

More information

CS 311 Homework 3 due 16:30, Thursday, 14 th October 2010

CS 311 Homework 3 due 16:30, Thursday, 14 th October 2010 CS 311 Homework 3 due 16:30, Thursdy, 14 th Octoer 2010 Homework must e sumitted on pper, in clss. Question 1. [15 pts.; 5 pts. ech] Drw stte digrms for NFAs recognizing the following lnguges:. L = {w

More information

Formal languages, automata, and theory of computation

Formal languages, automata, and theory of computation Mälrdlen University TEN1 DVA337 2015 School of Innovtion, Design nd Engineering Forml lnguges, utomt, nd theory of computtion Thursdy, Novemer 5, 14:10-18:30 Techer: Dniel Hedin, phone 021-107052 The exm

More information

Non-Deterministic Finite Automata. Fall 2018 Costas Busch - RPI 1

Non-Deterministic Finite Automata. Fall 2018 Costas Busch - RPI 1 Non-Deterministic Finite Automt Fll 2018 Costs Busch - RPI 1 Nondeterministic Finite Automton (NFA) Alphbet ={} q q2 1 q 0 q 3 Fll 2018 Costs Busch - RPI 2 Nondeterministic Finite Automton (NFA) Alphbet

More information

Lexical Analysis Finite Automate

Lexical Analysis Finite Automate Lexicl Anlysis Finite Automte CMPSC 470 Lecture 04 Topics: Deterministic Finite Automt (DFA) Nondeterministic Finite Automt (NFA) Regulr Expression NFA DFA A. Finite Automt (FA) FA re grph, like trnsition

More information

CS241 Week 6 Tutorial Solutions

CS241 Week 6 Tutorial Solutions 241 Week 6 Tutoril olutions Lnguges: nning & ontext-free Grmmrs Winter 2018 1 nning Exerises 1. 0x0x0xd HEXINT 0x0 I x0xd 2. 0xend--- HEXINT 0xe I nd ER -- MINU - 3. 1234-120x INT 1234 INT -120 I x 4.

More information

Hybrid Systems Modeling, Analysis and Control

Hybrid Systems Modeling, Analysis and Control Hyrid Systems Modeling, Anlysis nd Control Rdu Grosu Vienn University of Tehnology Leture 5 Finite Automt s Liner Systems Oservility, Rehility nd More Miniml DFA re Not Miniml NFA (Arnold, Diky nd Nivt

More information

CMSC 330: Organization of Programming Languages

CMSC 330: Organization of Programming Languages CMSC 330: Orgniztion of Progrmming Lnguges Finite Automt 2 CMSC 330 1 Types of Finite Automt Deterministic Finite Automt (DFA) Exctly one sequence of steps for ech string All exmples so fr Nondeterministic

More information

Compiler Design. Spring Lexical Analysis. Sample Exercises and Solutions. Prof. Pedro C. Diniz

Compiler Design. Spring Lexical Analysis. Sample Exercises and Solutions. Prof. Pedro C. Diniz University of Southern Cliforni Computer Siene Deprtment Compiler Design Spring 7 Lexil Anlysis Smple Exerises nd Solutions Prof. Pedro C. Diniz USC / Informtion Sienes Institute 47 Admirlty Wy, Suite

More information

Regular Expressions (RE) Regular Expressions (RE) Regular Expressions (RE) Regular Expressions (RE) Kleene-*

Regular Expressions (RE) Regular Expressions (RE) Regular Expressions (RE) Regular Expressions (RE) Kleene-* Regulr Expressions (RE) Regulr Expressions (RE) Empty set F A RE denotes the empty set Opertion Nottion Lnguge UNIX Empty string A RE denotes the set {} Alterntion R +r L(r ) L(r ) r r Symol Alterntion

More information

Finite Automata-cont d

Finite Automata-cont d Automt Theory nd Forml Lnguges Professor Leslie Lnder Lecture # 6 Finite Automt-cont d The Pumping Lemm WEB SITE: http://ingwe.inghmton.edu/ ~lnder/cs573.html Septemer 18, 2000 Exmple 1 Consider L = {ww

More information

Petri Nets. Rebecca Albrecht. Seminar: Automata Theory Chair of Software Engeneering

Petri Nets. Rebecca Albrecht. Seminar: Automata Theory Chair of Software Engeneering Petri Nets Ree Alreht Seminr: Automt Theory Chir of Softwre Engeneering Overview 1. Motivtion: Why not just using finite utomt for everything? Wht re Petri Nets nd when do we use them? 2. Introdution:

More information

Automata Theory 101. Introduction. Outline. Introduction Finite Automata Regular Expressions ω-automata. Ralf Huuck.

Automata Theory 101. Introduction. Outline. Introduction Finite Automata Regular Expressions ω-automata. Ralf Huuck. Outline Automt Theory 101 Rlf Huuck Introduction Finite Automt Regulr Expressions ω-automt Session 1 2006 Rlf Huuck 1 Session 1 2006 Rlf Huuck 2 Acknowledgement Some slides re sed on Wolfgng Thoms excellent

More information

Non-deterministic Finite Automata

Non-deterministic Finite Automata Non-deterministic Finite Automt Eliminting non-determinism Rdoud University Nijmegen Non-deterministic Finite Automt H. Geuvers nd T. vn Lrhoven Institute for Computing nd Informtion Sciences Intelligent

More information

NFAs continued, Closure Properties of Regular Languages

NFAs continued, Closure Properties of Regular Languages Algorithms & Models of Computtion CS/ECE 374, Fll 2017 NFAs continued, Closure Properties of Regulr Lnguges Lecture 5 Tuesdy, Septemer 12, 2017 Sriel Hr-Peled (UIUC) CS374 1 Fll 2017 1 / 31 Regulr Lnguges,

More information

ɛ-closure, Kleene s Theorem,

ɛ-closure, Kleene s Theorem, DEGefW5wiGH2XgYMEzUKjEmtCDUsRQ4d 1 A nice pper relevnt to this course is titled The Glory of the Pst 2 NICTA Resercher, Adjunct t the Austrlin Ntionl University nd Griffith University ɛ-closure, Kleene

More information

CS103B Handout 18 Winter 2007 February 28, 2007 Finite Automata

CS103B Handout 18 Winter 2007 February 28, 2007 Finite Automata CS103B ndout 18 Winter 2007 Ferury 28, 2007 Finite Automt Initil text y Mggie Johnson. Introduction Severl childrens gmes fit the following description: Pieces re set up on plying ord; dice re thrown or

More information

1. For each of the following theorems, give a two or three sentence sketch of how the proof goes or why it is not true.

1. For each of the following theorems, give a two or three sentence sketch of how the proof goes or why it is not true. York University CSE 2 Unit 3. DFA Clsses Converting etween DFA, NFA, Regulr Expressions, nd Extended Regulr Expressions Instructor: Jeff Edmonds Don t chet y looking t these nswers premturely.. For ech

More information

CS375: Logic and Theory of Computing

CS375: Logic and Theory of Computing CS375: Logic nd Theory of Computing Fuhu (Frnk) Cheng Deprtment of Computer Science University of Kentucky 1 Tble of Contents: Week 1: Preliminries (set lgebr, reltions, functions) (red Chpters 1-4) Weeks

More information

Chapter 2 Finite Automata

Chapter 2 Finite Automata Chpter 2 Finite Automt 28 2.1 Introduction Finite utomt: first model of the notion of effective procedure. (They lso hve mny other pplictions). The concept of finite utomton cn e derived y exmining wht

More information

NFA DFA Example 3 CMSC 330: Organization of Programming Languages. Equivalence of DFAs and NFAs. Equivalence of DFAs and NFAs (cont.

NFA DFA Example 3 CMSC 330: Organization of Programming Languages. Equivalence of DFAs and NFAs. Equivalence of DFAs and NFAs (cont. NFA DFA Exmple 3 CMSC 330: Orgniztion of Progrmming Lnguges NFA {B,D,E {A,E {C,D {E Finite Automt, con't. R = { {A,E, {B,D,E, {C,D, {E 2 Equivlence of DFAs nd NFAs Any string from {A to either {D or {CD

More information

Types of Finite Automata. CMSC 330: Organization of Programming Languages. Comparing DFAs and NFAs. NFA for (a b)*abb.

Types of Finite Automata. CMSC 330: Organization of Programming Languages. Comparing DFAs and NFAs. NFA for (a b)*abb. CMSC 330: Orgniztion of Progrmming Lnguges Finite Automt 2 Types of Finite Automt Deterministic Finite Automt () Exctly one sequence of steps for ech string All exmples so fr Nondeterministic Finite Automt

More information

State Minimization for DFAs

State Minimization for DFAs Stte Minimiztion for DFAs Red K & S 2.7 Do Homework 10. Consider: Stte Minimiztion 4 5 Is this miniml mchine? Step (1): Get rid of unrechle sttes. Stte Minimiztion 6, Stte is unrechle. Step (2): Get rid

More information

Types of Finite Automata. CMSC 330: Organization of Programming Languages. Comparing DFAs and NFAs. Comparing DFAs and NFAs (cont.) Finite Automata 2

Types of Finite Automata. CMSC 330: Organization of Programming Languages. Comparing DFAs and NFAs. Comparing DFAs and NFAs (cont.) Finite Automata 2 CMSC 330: Orgniztion of Progrmming Lnguges Finite Automt 2 Types of Finite Automt Deterministic Finite Automt () Exctly one sequence of steps for ech string All exmples so fr Nondeterministic Finite Automt

More information

Finite Automata Theory and Formal Languages TMV027/DIT321 LP4 2018

Finite Automata Theory and Formal Languages TMV027/DIT321 LP4 2018 Finite Automt Theory nd Forml Lnguges TMV027/DIT321 LP4 2018 Lecture 10 An Bove April 23rd 2018 Recp: Regulr Lnguges We cn convert between FA nd RE; Hence both FA nd RE ccept/generte regulr lnguges; More

More information

Non-deterministic Finite Automata

Non-deterministic Finite Automata Non-deterministic Finite Automt From Regulr Expressions to NFA- Eliminting non-determinism Rdoud University Nijmegen Non-deterministic Finite Automt H. Geuvers nd J. Rot Institute for Computing nd Informtion

More information

Compiler Design. Fall Lexical Analysis. Sample Exercises and Solutions. Prof. Pedro C. Diniz

Compiler Design. Fall Lexical Analysis. Sample Exercises and Solutions. Prof. Pedro C. Diniz University of Southern Cliforni Computer Science Deprtment Compiler Design Fll Lexicl Anlysis Smple Exercises nd Solutions Prof. Pedro C. Diniz USC / Informtion Sciences Institute 4676 Admirlty Wy, Suite

More information

12.1 Nondeterminism Nondeterministic Finite Automata. a a b ε. CS125 Lecture 12 Fall 2016

12.1 Nondeterminism Nondeterministic Finite Automata. a a b ε. CS125 Lecture 12 Fall 2016 CS125 Lecture 12 Fll 2016 12.1 Nondeterminism The ide of nondeterministic computtions is to llow our lgorithms to mke guesses, nd only require tht they ccept when the guesses re correct. For exmple, simple

More information

CS:4330 Theory of Computation Spring Regular Languages. Equivalences between Finite automata and REs. Haniel Barbosa

CS:4330 Theory of Computation Spring Regular Languages. Equivalences between Finite automata and REs. Haniel Barbosa CS:4330 Theory of Computtion Spring 208 Regulr Lnguges Equivlences between Finite utomt nd REs Hniel Brbos Redings for this lecture Chpter of [Sipser 996], 3rd edition. Section.3. Finite utomt nd regulr

More information

input tape head moves current state

input tape head moves current state CPS 140 - Mthemticl Foundtions of CS Dr. Susn Rodger Section: Finite Automt (Ch. 2) (lecture notes) Things to do in clss tody (Jn. 13, 2004): ffl questions on homework 1 ffl finish chpter 1 ffl Red Chpter

More information

Today s Topics Automata and Languages

Today s Topics Automata and Languages Tody s Topics Automt nd Lnguges Prof. Mohmed Hmd Softwre Engineering L. The University of Aizu Jpn DFA to Regulr Expression GFNA DFAèGNFA GNFA è RE DFA è RE Exmples 2 DFA è RE NFA DFA -NFA REX GNFA 3 Definition

More information

Automata and Languages

Automata and Languages Automt nd Lnguges Prof. Mohmed Hmd Softwre Engineering L. The University of Aizu Jpn Tody s Topics DFA to Regulr Expression GFNA DFAèGNFA GNFA è RE DFA è RE Exmples 2 DFA è RE NFA DFA -NFA REX GNFA 3 Definition

More information

Anatomy of a Deterministic Finite Automaton. Deterministic Finite Automata. A machine so simple that you can understand it in less than one minute

Anatomy of a Deterministic Finite Automaton. Deterministic Finite Automata. A machine so simple that you can understand it in less than one minute Victor Admchik Dnny Sletor Gret Theoreticl Ides In Computer Science CS 5-25 Spring 2 Lecture 2 Mr 3, 2 Crnegie Mellon University Deterministic Finite Automt Finite Automt A mchine so simple tht you cn

More information

Converting Regular Expressions to Discrete Finite Automata: A Tutorial

Converting Regular Expressions to Discrete Finite Automata: A Tutorial Converting Regulr Expressions to Discrete Finite Automt: A Tutoril Dvid Christinsen 2013-01-03 This is tutoril on how to convert regulr expressions to nondeterministic finite utomt (NFA) nd how to convert

More information