Refined interfaces for compositional verification
|
|
- Edwin Walton
- 6 years ago
- Views:
Transcription
1 Refined interfces for compositionl verifiction Frédéric Lng INRI Rhône-lpes
2 Motivtion Enumertive verifiction of concurrent systems Prllel composition of synchronous processes Systemtic explortion of the stte/trnsition grph obtined by interleving nd synchroniztion ompositionl verifiction to pllite stte explosion Simple: reduce stte/trnsition grphs incrementlly Enhnced: use interfce constrints to void intermedite stte explosion This tlk is bout tool to build interfce constrints utomticlly 2
3 Stte/trnsition grphs Semntic model of ction-bsed processes, lso clled Lbelled Trnsition System (LTS) Trnsitions between sttes re lbelled by events Synchronizble/observble events Non-synchronizble/hidden event τ b c τ c P toolbox llows on-the-fly explortion of stte/trnsition grphs (OPEN/ESR) 3
4 Using interfce constrints big grph P cn be reduced using interfce constrints, represented s grph I nd set of lbels through which P nd I interct Projection opertor P I (Grf & Steffen, Krimm & Mounier) omputes the sub-grph of P rechble in P I I cn be reduced modulo sfety equivlence fter hiding ll lbels outside similr pproch exists for SP (heung & Krmer) Norml prllel composition insted of projection Requires tu elimintion nd determiniztion (expensive) in I to ensure context trnsprency 4
5 5 Exmple of projection {,, } =
6 The PROJETOR tool of P Softwre implementtion of projection (Krimm & Mounier 1997) OPEN/ESR grph P G grph (interfce) I Synchroniztion set PROJETOR G Grph P I 6
7 omputing the interfce constrints Solution 1: User-specified interfce The user provides n interfce correct interfce is hrd to guess ut correctness cn be checked fterwrds Solution 2: "Exct" interfce correct interfce is computed utomticlly from the environment Krimm & Mounier give n lgorithm bsed on n nlysis of the lgebric LOTOS-like expression describing the composition of processes The interfce I is process of the composition The synchroniztion set is derived utomticlly 7
8 Limittion 1 of K&M lgorithm The method to compute the synchroniztion set is specific to LOTOS prllel composition How cn we build exct interfces in expressions tht use different nd/or more generl opertors? 8
9 Limittion 2 of K&M lgorithm It is impossible to compute interfce constrints induced by combintion of (distnt) processes Sometimes, only such constrints llow reductions Exmple: in b c {, b, d} ( {c, d} ) b d d P 1 P 2 P 3 restricting P 3 w.r.t. either P 1 or P 2 yields no reduction: P 3 {, d} P 1 = P 3 {c, d} P 2 = P 3 Using n interfce obtined by combintion of P 1 nd P 2 (synchronized on b) would yield better reductions d c c d c 9
10 Limittion 3 of K&M lgorithm Interfces my be not precise enough when nondeterministic synchroniztion is involved Exmple: in b b Restricting P 2 w.r.t. P 1 yields no reduction: P 2 {} P 1 = P 2 However P 1 implies tht two successive b ctions cnnot be reched without n in between b, b b {, b} ( {} ) P 1 P 2 P 3 d 10
11 Refined interfces We propose new lgorithm which solves the limittions of K&M lgorithm The lgorithm works in three phses 1. Trnsltion of the composition of processes into generl model clled "synchroniztion networks" 2. Extrction of n "interfce network" from the network model 3. Genertion of the interfce grph corresponding to the interfce network 11
12 Phse 1: synchroniztion networks generl synchroniztion model Synchroniztion of processes P 1,..., P n described by set of synchroniztion vectors of the form where L i,1,..., L i,n L i ech L i,j is either lbel of P j or the specil symbol denoting inction of P j L i is the lbel used in the product grph s the result of the synchroniztion between the P j 's 12
13 Exmple 1 d b c d d ( c c c b ) {, b, d} {c, d} d P 1 P 2 P 3 cn be represented by the set of synchroniztion vectors,, b, b, b, c, c c d, d, d d 13
14 Exmple 2 b b b, b b {, b} ( {} ) d P 1 P 2 P 3 cn be represented by the set of synchroniztion vectors,, b, b, b b,, b b,, d d } nondeterministic synchroniztion on b for P 1 14
15 Phse 2: Interfce network extrction Extrction of network N' representing n bstrction of the environment of process to be constrined Inputs: The synchroniztion network N of system P 1,..., P n The index i of the process P i to be constrined The indices j 1,..., j m (user-given) of the constrining processes lgorithm: for ech vector v in N, crete in N' vector v[j 1 ],..., v[j m ] r where r = v[i] if v[i] (P i ctive in synchroniztion) r = τ otherwise 15
16 Exmple P1, P2, P3 synchronized by the vectors,, b, b, b b,, b b,, d d The interfce network of P2 induced by P1 is: b b b τ τ (This lst one cn be removed) 16
17 Phse 3: interfce grph genertion Generte the grph corresponding to N' (product of P j1,..., P jm ) Thnks to congruence, P j1,..., P jm cn be reduced modulo sfety equivlence beforehnd Prtil order reduction llows to void useless interlevings 17
18 Using the generted interfce The (possibly lrge) grph of P i cn be replced by (smller) grph of P i I where I is n interfce obtined by our lgorithm Forml proof provided in FORTE'2006 pper 18
19 Limittion 1 solved The lgorithm pplies on synchroniztion networks, generl model similr to ME nd F2 networks We implemented the trnsltion into networks for S, SP, LOTOS, mrl prllel composition E-LOTOS generlized prllel composition nd m mong n synchroniztion The trnsltion cn still be done for other opertors 19
20 Limittion 2 solved Interfce constrints induced by ny combintion of processes cn be computed Exmple: in b c d d ( c c c ) {, b, d} b {c, d} d d P 1 P 2 P 3 the interfce I of P 3 induced by P 1 nd P 2 is: c τ c d d c It yields reduction of P 3 s P 3 {, c, d} I = c 20
21 Limittion 3 solved Interfces re precise even in presence of nondeterministic synchroniztion, b b {, b} ( {} ) b b b d P 1 P 2 P 3 The interfce I of P 2 induced by P 1 is: b τ It yields reduction of P 2 s P 2 {, b} I = b 21
22 Implementtion in P lgorithm implemented in Exp.Open 2.0 (-interfce option) Exmple: odp.exp hide ll but WORK in pr EXPORT, IMPORT in pr WORK #2 in "object_1.bcg" "object_2.bcg" "object_3.bcg" "object_4.bcg" end pr "trder.bcg" end pr end hide 22
23 Implementtion in P exp.open -wektrce -interfce "5: 1 2 3" "odp.exp" genertor "trder_interfce.bcg" Genertes n interfce grph "trder_interfce.bcg" induced by the 1st ("object_1.bcg"), 2nd ("object_2.bcg"), nd 3rd ("object_3.bcg") grphs in "odp.exp" The interfce grph cn be used to constrin the 5th grph ("trder.bcg") Prtil order reduction (persistent set method) preserving observble trces is pplied 23
24 pplictions (1/3) Philips' HVi Home udio-video leder election Modeled in LOTOS by J. Romijn (Eindhoven) Lrgest process (404,477 sttes) ws: Reduced downto 365,923 sttes (182s, 46Mb) using interfce obtined by K&M lgorithm Reduced downto 645 sttes (11s, 8.5Mb) using refined interfce 24
25 pplictions (2/3) OP (Open istributed Processing) Trder Modeled in E-LOTOS by Grvel & Sighirenu (INRI) Uses m mong n synchroniztion to model the dynmicity of object exchnges Trder reduced from 1 M sttes without interfce downto 256 sttes using refined interfce 25
26 pplictions (3/3) che oherency Protocol Modeled in LOTOS by M. Zendri (ull) 5 gents ccessing remote directory concurrently No reduction using interfce obtined by K&M lgorithm Remote directory reduced from 1 M sttes downto 60 sttes using refined interfce irectory generted for configurtion with 7 gents (81 sttes) 26
27 Refined bstrction in SVL Refined interfce genertion nd projection cn be done esily within the SVL scripting lnguge New "refined bstrction" opertor clls EXP.OPEN nd PROJETOR utomticlly Exmple: "cche.bcg" = root lef strong reduction of ( (GENT_1 GENT_2 GENT_3) [GET_LINE_STTUS, PUT_LINE_STTUS] (refined bstrction GENT_1, GENT_2 using IR_STRT of IRETORY) ); 27
28 onclusions We provided new lgorithm to synthesize interfce constrints utomticlly The lgorithm solves the 3 limittions of K&M's lgorithm It does not depend on prticulr input lnguge It permits to tke into ccount constrints induced by combintion of distnt processes It permits finer nlysis of synchroniztion ptterns between processes, thus yielding better reductions The method is fully implemented in P It is esy to use thnks to the SVL scripting lnguge Experiments indicte possible reductions by severl orders of mgnitude 28
Notes on specifying systems in EST
Robert Meolic, Ttjn Kpus: Notes on specifying systems in EST 1 Notes on specifying systems in EST Robert Meolic, Ttjn Kpus Fculty of EE & CS University of Mribor Robert Meolic, Ttjn Kpus: Notes on specifying
More informationBisimulation. R.J. van Glabbeek
Bisimultion R.J. vn Glbbeek NICTA, Sydney, Austrli. School of Computer Science nd Engineering, The University of New South Wles, Sydney, Austrli. Computer Science Deprtment, Stnford University, CA 94305-9045,
More informationStrong Bisimulation. Overview. References. Actions Labeled transition system Transition semantics Simulation Bisimulation
Strong Bisimultion Overview Actions Lbeled trnsition system Trnsition semntics Simultion Bisimultion References Robin Milner, Communiction nd Concurrency Robin Milner, Communicting nd Mobil Systems 32
More informationParse trees, ambiguity, and Chomsky normal form
Prse trees, miguity, nd Chomsky norml form In this lecture we will discuss few importnt notions connected with contextfree grmmrs, including prse trees, miguity, nd specil form for context-free grmmrs
More informationLearning Moore Machines from Input-Output Traces
Lerning Moore Mchines from Input-Output Trces Georgios Gintmidis 1 nd Stvros Tripkis 1,2 1 Alto University, Finlnd 2 UC Berkeley, USA Motivtion: lerning models from blck boxes Inputs? Lerner Forml Model
More informationFormal Languages Simplifications of CFGs
Forml Lnguges implifictions of CFGs ubstitution Rule Equivlent grmmr b bc ubstitute b bc bbc b 2 ubstitution Rule b bc bbc ubstitute b bc bbc bc Equivlent grmmr 3 In generl: xz y 1 ubstitute y 1 xz xy1z
More informationSummer School Verification Technology, Systems & Applications
VTSA 2011 Summer School Verifiction Technology, Systems & Applictions 4th edition since 2008: Liège (Belgium), Sep. 19 23, 2011 free prticiption, limited number of prticipnts ppliction dedline: July 22,
More informationReinforcement learning II
CS 1675 Introduction to Mchine Lerning Lecture 26 Reinforcement lerning II Milos Huskrecht milos@cs.pitt.edu 5329 Sennott Squre Reinforcement lerning Bsics: Input x Lerner Output Reinforcement r Critic
More informationFinite 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 informationLecture 3 ( ) (translated and slightly adapted from lecture notes by Martin Klazar)
Lecture 3 (5.3.2018) (trnslted nd slightly dpted from lecture notes by Mrtin Klzr) Riemnn integrl Now we define precisely the concept of the re, in prticulr, the re of figure U(, b, f) under the grph of
More informationDesigning 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 informationTHE EXISTENCE-UNIQUENESS THEOREM FOR FIRST-ORDER DIFFERENTIAL EQUATIONS.
THE EXISTENCE-UNIQUENESS THEOREM FOR FIRST-ORDER DIFFERENTIAL EQUATIONS RADON ROSBOROUGH https://intuitiveexplntionscom/picrd-lindelof-theorem/ This document is proof of the existence-uniqueness theorem
More informationGood-for-Games Automata versus Deterministic Automata.
Good-for-Gmes Automt versus Deterministic Automt. Denis Kuperberg 1,2 Mich l Skrzypczk 1 1 University of Wrsw 2 IRIT/ONERA (Toulouse) Séminire MoVe 12/02/2015 LIF, Luminy Introduction Deterministic utomt
More informationManaging non-determinism in symbolic robot motion planning and control
2007 IEEE Interntionl Conference on Robotics nd Automtion Rom, Itly, 10 14 April 2007 ThD11.4 Mnging non-determinism in symbolic robot motion plnning nd control Mrius Kloetzer nd Clin Belt Center for Informtion
More informationChapter 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 informationHow to simulate Turing machines by invertible one-dimensional cellular automata
How to simulte Turing mchines by invertible one-dimensionl cellulr utomt Jen-Christophe Dubcq Déprtement de Mthémtiques et d Informtique, École Normle Supérieure de Lyon, 46, llée d Itlie, 69364 Lyon Cedex
More informationNormal Forms for Context-free Grammars
Norml Forms for Context-free Grmmrs 1 Linz 6th, Section 6.2 wo Importnt Norml Forms, pges 171--178 2 Chomsky Norml Form All productions hve form: A BC nd A vrile vrile terminl 3 Exmples: S AS S AS S S
More informationNon-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 informationInforme Técnico / Technical Report
DEPARTAMENTO DE SISTEMAS INFORMÁTICOS Y COMPUTACIÓN UNIVERSIDAD POLITÉCNICA DE VALENCIA P.O. Box: 22012 E-46071 Vlenci (SPAIN) Informe Técnico / Technicl Report Ref. No.: DSIC-II/03/10 Pges: 30 Title:
More informationConcepts of Concurrent Computation Spring 2015 Lecture 9: Petri Nets
Concepts of Concurrent Computtion Spring 205 Lecture 9: Petri Nets Sebstin Nnz Chris Poskitt Chir of Softwre Engineering Petri nets Petri nets re mthemticl models for describing systems with concurrency
More informationTheory 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 informationCS375: 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 informationGlobal Types for Dynamic Checking of Protocol Conformance of Multi-Agent Systems
Globl Types for Dynmic Checking of Protocol Conformnce of Multi-Agent Systems (Extended Abstrct) Dvide Ancon, Mtteo Brbieri, nd Vivin Mscrdi DIBRIS, University of Genov, Itly emil: dvide@disi.unige.it,
More informationConvert the NFA into DFA
Convert the NF into F For ech NF we cn find F ccepting the sme lnguge. The numer of sttes of the F could e exponentil in the numer of sttes of the NF, ut in prctice this worst cse occurs rrely. lgorithm:
More informationSemantic Reachability. Richard Mayr. Institut fur Informatik. Technische Universitat Munchen. Arcisstr. 21, D Munchen, Germany E. N. T. C. S.
URL: http://www.elsevier.nl/locte/entcs/volume6.html?? pges Semntic Rechbility Richrd Myr Institut fur Informtik Technische Universitt Munchen Arcisstr. 21, D-80290 Munchen, Germny e-mil: myrri@informtik.tu-muenchen.de
More informationSection 14.3 Arc Length and Curvature
Section 4.3 Arc Length nd Curvture Clculus on Curves in Spce In this section, we ly the foundtions for describing the movement of n object in spce.. Vector Function Bsics In Clc, formul for rc length in
More informationCS 275 Automata and Formal Language Theory
CS 275 Automt nd Forml Lnguge Theory Course Notes Prt II: The Recognition Problem (II) Chpter II.5.: Properties of Context Free Grmmrs (14) Anton Setzer (Bsed on book drft by J. V. Tucker nd K. Stephenson)
More informationTheory 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 informationSAT-Solving in CSP Trace Refinement
ST-Solving in CSP Trce Refinement Hristin Plikrev, Joël Ouknine nd. W. Roscoe Deprtment of Computer Science, Oxford University, UK bstrct In this pper, we ddress the problem of pplying ST-bsed bounded
More information12.1 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 informationCalculating τ-confluence Compositionally
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE Clculting -Confluence Compositionlly Gordon Pce Frédéric Lng Rdu Mteescu N 4918 Septembre 2003 THÈME 1 ISSN 0249-6399 ISRN INRIA/RR--4918--FR+ENG
More informationGlobal Session Types for Dynamic Checking of Protocol Conformance of Multi-Agent Systems
Globl Session Types for Dynmic Checking of Protocol Conformnce of Multi-Agent Systems (Extended Abstrct) Dvide Ancon, Mtteo Brbieri, nd Vivin Mscrdi DIBRIS, University of Genov, Itly emil: dvide@disi.unige.it,
More informationTowards High-Level Specification & Synthesis of Dynamic Process Logic
Towrds High-Level Specifiction & Synthesis of Dynmic Process Logic Oliver Diessel Usm Mlik Keith So George Milne School of Computer Science nd Engineering, The University of New South Wles, Austrli School
More informationProcess Algebra CSP A Technique to Model Concurrent Programs
Process Algebr CSP A Technique to Model Concurrent Progrms Jnury 15, 2002 Hui Shi 1 Contents CSP-Processes Opertionl Semntics Trnsition systems nd stte mchines Bisimultion Firing rules for CSP Model-Checker
More informationCentrum voor Wiskunde en Informatica REPORTRAPPORT. Supervisory control for nondeterministic systems
Centrum voor Wiskunde en Informtic REPORTRAPPORT Supervisory control for nondeterministic systems A. Overkmp Deprtment of Opertions Reserch, Sttistics, nd System Theory BS-R9411 1994 Supervisory Control
More informationFrobenius numbers of generalized Fibonacci semigroups
Frobenius numbers of generlized Fiboncci semigroups Gretchen L. Mtthews 1 Deprtment of Mthemticl Sciences, Clemson University, Clemson, SC 29634-0975, USA gmtthe@clemson.edu Received:, Accepted:, Published:
More informationNon 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 informationChapter 5 Plan-Space Planning
Lecture slides for Automted Plnning: Theory nd Prctice Chpter 5 Pln-Spce Plnning Dn S. Nu CMSC 722, AI Plnning University of Mrylnd, Spring 2008 1 Stte-Spce Plnning Motivtion g 1 1 g 4 4 s 0 g 5 5 g 2
More information1 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 informationCSCI 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 informationSemantic reachability for simple process algebras. Richard Mayr. Abstract
Semntic rechbility for simple process lgebrs Richrd Myr Abstrct This pper is n pproch to combine the rechbility problem with semntic notions like bisimultion equivlence. It dels with questions of the following
More informationCS415 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 informationJin-Fu Li. Department of Electrical Engineering National Central University Jhongli, Taiwan
Trnsprent BIST for RAMs Jin-Fu Li Advnced d Relible Systems (ARES) Lb. Deprtment of Electricl Engineering Ntionl Centrl University Jhongli, Tiwn Outline Introduction Concept of Trnsprent Test Trnsprent
More information1.4 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 informationMinimal 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 information12.1 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 informationCS 267: Automated Verification. Lecture 8: Automata Theoretic Model Checking. Instructor: Tevfik Bultan
CS 267: Automted Verifiction Lecture 8: Automt Theoretic Model Checking Instructor: Tevfik Bultn LTL Properties Büchi utomt [Vrdi nd Wolper LICS 86] Büchi utomt: Finite stte utomt tht ccept infinite strings
More informationStuttering for Abstract Probabilistic Automata
Stuttering for Abstrct Probbilistic Automt Benoît Delhye 1, Kim G. Lrsen 2, nd Axel Legy 1 1 INRIA/IRISA, Frnce, {benoit.delhye,xel.legy}@inri.fr 2 Alborg University, Denmrk, kgl@cs.u.dk Abstrct. Probbilistic
More informationChapter 4 Contravariance, Covariance, and Spacetime Diagrams
Chpter 4 Contrvrince, Covrince, nd Spcetime Digrms 4. The Components of Vector in Skewed Coordintes We hve seen in Chpter 3; figure 3.9, tht in order to show inertil motion tht is consistent with the Lorentz
More informationSafety Controller Synthesis for Switched Systems using Multiscale Symbolic Models
Sfety Controller Synthesis for Switched Systems using Multiscle Symolic Models Antoine Girrd Lortoire des Signux et Systèmes Gif sur Yvette, Frnce Séminire du LAAS Toulouse, 29 Juin, 2016 A. Girrd (L2S-CNRS)
More informationIntroduction to spefication and verification Lecture Notes, autumn 2011
Introduction to spefiction nd verifiction Lecture Notes, utumn 2011 Timo Krvi UNIVERSITY OF HELSINKI FINLAND Contents 1 Introduction 1 1.1 The strting point............................ 1 1.2 Globl stte
More informationCoalgebra, Lecture 15: Equations for Deterministic Automata
Colger, Lecture 15: Equtions for Deterministic Automt Julin Slmnc (nd Jurrin Rot) Decemer 19, 2016 In this lecture, we will study the concept of equtions for deterministic utomt. The notes re self contined
More informationLTL Translation Improvements in Spot
LTL Trnsltion Improvements in Spot Alexndre Duret-Lutz http://www.lrde.epit.fr/~dl/ VECoS'11 16 September 2011 Alexndre Duret-Lutz LTL Trnsltion Improvements 1 / 19 Context High-level
More informationCS 275 Automata and Formal Language Theory
CS 275 Automt nd Forml Lnguge Theory Course Notes Prt II: The Recognition Problem (II) Chpter II.6.: Push Down Automt Remrk: This mteril is no longer tught nd not directly exm relevnt Anton Setzer (Bsed
More informationCS 275 Automata and Formal Language Theory
CS 275 utomt nd Forml Lnguge Theory Course Notes Prt II: The Recognition Prolem (II) Chpter II.5.: Properties of Context Free Grmmrs (14) nton Setzer (Bsed on ook drft y J. V. Tucker nd K. Stephenson)
More informationUninformed Search Lecture 4
Lecture 4 Wht re common serch strtegies tht operte given only serch problem? How do they compre? 1 Agend A quick refresher DFS, BFS, ID-DFS, UCS Unifiction! 2 Serch Problem Formlism Defined vi the following
More informationEvent Structures for Arbitrary Disruption
Fundment Informtice XX (2005) 1 28 1 IOS Press Event Structures for Arbitrry Disruption Hrld Fecher Christin Albrecht Universität zu Kiel Technische Fkultät, Institut für Informtik, Hermnn-Rodewldstr.
More informationFormal 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 informationNon Deterministic Automata. Formal Languages and Automata - Yonsei CS 1
Non Deterministic Automt Forml Lnguges nd Automt - Yonsei CS 1 Nondeterministic Finite Accepter (NFA) We llow set of possible moves insted of A unique move. Alphbet = {} Two choices q 1 q2 Forml Lnguges
More informationCommunication à un colloque (Conference Paper)
Communiction à un colloque (Conference Pper) "Lerning system bstrctions for humn opertors" Combéfis, Sébstien ; Ginnkopoulou, Dimitr ; Pecheur, Chrles ; Fery, Michel Abstrct This pper is concerned with
More informationReal-time Concepts for a Formal Specification Language for Software / Hardware Systems
1 Rel-time Concepts for Forml Specifiction Lnguge for Softwre / Hrdwre Systems M.C.W. Geilen nd J.P.M. Voeten Abstrct Incresingly complex systems re being designed tht consist of concurrently operting
More informationAutomata 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 informationFinite Automata. Informatics 2A: Lecture 3. John Longley. 22 September School of Informatics University of Edinburgh
Lnguges nd Automt Finite Automt Informtics 2A: Lecture 3 John Longley School of Informtics University of Edinburgh jrl@inf.ed.c.uk 22 September 2017 1 / 30 Lnguges nd Automt 1 Lnguges nd Automt Wht is
More informationExtended nonlocal games from quantum-classical games
Extended nonlocl gmes from quntum-clssicl gmes Theory Seminr incent Russo niversity of Wterloo October 17, 2016 Outline Extended nonlocl gmes nd quntum-clssicl gmes Entngled vlues nd the dimension of entnglement
More informationProbabilistic Model Checking Michaelmas Term Dr. Dave Parker. Department of Computer Science University of Oxford
Probbilistic Model Checking Michelms Term 2011 Dr. Dve Prker Deprtment of Computer Science University of Oxford Long-run properties Lst lecture: regulr sfety properties e.g. messge filure never occurs
More informationHennessy-Milner Logic 1.
Hennessy-Milner Logic 1. Colloquium in honor of Robin Milner. Crlos Olrte. Pontifici Universidd Jverin 28 April 2010. 1 Bsed on the tlks: [1,2,3] Prof. Robin Milner (R.I.P). LIX, Ecole Polytechnique. Motivtion
More informationConjunction on processes: Full abstraction via ready-tree semantics
Theoreticl Computer Science 373 (2007) 19 40 www.elsevier.com/locte/tcs Conjunction on processes: Full bstrction vi redy-tree semntics Gerld Lüttgen, Wlter Vogler b, Deprtment of Computer Science, University
More informationNFAs and Regular Expressions. NFA-ε, continued. Recall. Last class: Today: Fun:
CMPU 240 Lnguge Theory nd Computtion Spring 2019 NFAs nd Regulr Expressions Lst clss: Introduced nondeterministic finite utomt with -trnsitions Tody: Prove n NFA- is no more powerful thn n NFA Introduce
More informationLecture 9: LTL and Büchi Automata
Lecture 9: LTL nd Büchi Automt 1 LTL Property Ptterns Quite often the requirements of system follow some simple ptterns. Sometimes we wnt to specify tht property should only hold in certin context, clled
More informationJonathan Mugan. July 15, 2013
Jonthn Mugn July 15, 2013 Imgine rt in Skinner box. The rt cn see screen of imges, nd dot in the lower-right corner determines if there will be shock. Bottom-up methods my not find this dot, but top-down
More informationCS: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 informationInfinite Geometric Series
Infinite Geometric Series Finite Geometric Series ( finite SUM) Let 0 < r < 1, nd let n be positive integer. Consider the finite sum It turns out there is simple lgebric expression tht is equivlent to
More information1 Online Learning and Regret Minimization
2.997 Decision-Mking in Lrge-Scle Systems My 10 MIT, Spring 2004 Hndout #29 Lecture Note 24 1 Online Lerning nd Regret Minimiztion In this lecture, we consider the problem of sequentil decision mking in
More informationFABER Formal Languages, Automata and Models of Computation
DVA337 FABER Forml Lnguges, Automt nd Models of Computtion Lecture 5 chool of Innovtion, Design nd Engineering Mälrdlen University 2015 1 Recp of lecture 4 y definition suset construction DFA NFA stte
More informationAUTOMATA 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 information19 Optimal behavior: Game theory
Intro. to Artificil Intelligence: Dle Schuurmns, Relu Ptrscu 1 19 Optiml behvior: Gme theory Adversril stte dynmics hve to ccount for worst cse Compute policy π : S A tht mximizes minimum rewrd Let S (,
More informationDefinite integral. Mathematics FRDIS MENDELU
Definite integrl Mthemtics FRDIS MENDELU Simon Fišnrová Brno 1 Motivtion - re under curve Suppose, for simplicity, tht y = f(x) is nonnegtive nd continuous function defined on [, b]. Wht is the re of the
More informationLexical 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 informationCS5371 Theory of Computation. Lecture 20: Complexity V (Polynomial-Time Reducibility)
CS5371 Theory of Computtion Lecture 20: Complexity V (Polynomil-Time Reducibility) Objectives Polynomil Time Reducibility Prove Cook-Levin Theorem Polynomil Time Reducibility Previously, we lernt tht if
More informationFinite Automata Part Three
Finite Automt Prt Three Hello Hello Wonderful Wonderful Condensed Condensed Slide Slide Reders! Reders! The The first first hlf hlf of of this this lecture lecture consists consists lmost lmost exclusively
More informationNon-Deterministic Finite Automata
Non-Deterministic Finite Automt http://users.comlb.ox.c.uk/luke. ong/teching/moc/nf2up.pdf 1 Nondeterministic Finite Automton (NFA) Alphbet ={} q1 q2 2 Alphbet ={} Two choices q1 q2 3 Alphbet ={} Two choices
More informationComponent Based Testing with ioco
CTIT Technicl Report TR CTIT 03 34, University of Twente, 2003 Component Bsed Testing with ioco Mchiel vn der Bijl 1, Arend Rensink 1 nd Jn Tretmns 2 1 Softwre Engineering, Deprtment of Computer Science,
More informationVerifying Concurrent Message-Passing C Programs with Recursive Calls
Verifying Concurrent Messge-Pssing C Progrms with Recursive Clls Sgr Chki Edmund Clrke Crnegie Mellon University Pittsburgh USA Nichols Kidd Thoms Reps University of Wisconsin Mdison USA Tyssir Touili
More informationKleene Theorems for Free Choice Nets Labelled with Distributed Alphabets
Kleene Theorems for Free Choice Nets Lbelled with Distributed Alphbets Rmchndr Phwde Indin Institute of Technology Dhrwd, Dhrwd 580011, Indi Emil: prb@iitdh.c.in Abstrct. We provided [15] expressions for
More informationA Formal Approach for Contextual Planning Management: Application to Smart Campus Environment.
A Forml Approch for Contextul Plnning Mngement: Appliction to Smrt Cmpus Environment Ahmed-Chwki Chouche, Aml El Fllh Seghrouchni, Jen-Michel Ilié, Djmel Eddine Sïdouni To cite this version: Ahmed-Chwki
More informationA From LTL to Deterministic Automata A Safraless Compositional Approach
A From LTL to Deterministic Automt A Sfrless Compositionl Approch JAVIER ESPARZA, Fkultät für Informtik, Technische Universität München, Germny JAN KŘETÍNSKÝ, IST Austri SALOMON SICKERT, Fkultät für Informtik,
More informationIntermediate Math Circles Wednesday, November 14, 2018 Finite Automata II. Nickolas Rollick a b b. a b 4
Intermedite Mth Circles Wednesdy, Novemer 14, 2018 Finite Automt II Nickols Rollick nrollick@uwterloo.c Regulr Lnguges Lst time, we were introduced to the ide of DFA (deterministic finite utomton), one
More informationFrom LTL to Symbolically Represented Deterministic Automata
Motivtion nd Prolem Setting Determinizing Non-Confluent Automt Det. vi Automt Hierrchy From LTL to Symoliclly Represented Deterministic Automt Andres Morgenstern Klus Schneider Sven Lmerti Mnuel Gesell
More informationJim Lambers MAT 169 Fall Semester Lecture 4 Notes
Jim Lmbers MAT 169 Fll Semester 2009-10 Lecture 4 Notes These notes correspond to Section 8.2 in the text. Series Wht is Series? An infinte series, usully referred to simply s series, is n sum of ll of
More informationFinite 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 informationSafety Controller Synthesis for Switched Systems using Multiscale Symbolic Models
Sfety Controller Synthesis for Switched Systems using Multiscle Symolic Models Antoine Girrd Lortoire des Signux et Systèmes Gif sur Yvette, Frnce Workshop on switching dynmics & verifiction Pris, Jnury
More informationEE273 Lecture 15 Asynchronous Design November 16, Today s Assignment
EE273 Lecture 15 Asynchronous Design Novemer 16, 199 Willim J. Dlly Computer Systems Lortory Stnford University illd@csl.stnford.edu 1 Tody s Assignment Term Project see project updte hndout on we checkpoint
More informationMath Lecture 23
Mth 8 - Lecture 3 Dyln Zwick Fll 3 In our lst lecture we delt with solutions to the system: x = Ax where A is n n n mtrix with n distinct eigenvlues. As promised, tody we will del with the question of
More informationRegular 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 informationFoundations for Timed Systems
Foundtions for Timed Systems Ptrici Bouyer LSV CNRS UMR 8643 & ENS de Cchn 6, venue du Président Wilson 9423 Cchn Frnce emil: bouyer@lsv.ens-cchn.fr Introduction Explicit timing constrints re nturlly present
More informationModule 6: LINEAR TRANSFORMATIONS
Module 6: LINEAR TRANSFORMATIONS. Trnsformtions nd mtrices Trnsformtions re generliztions of functions. A vector x in some set S n is mpped into m nother vector y T( x). A trnsformtion is liner if, for
More informationDuality # Second iteration for HW problem. Recall our LP example problem we have been working on, in equality form, is given below.
Dulity #. Second itertion for HW problem Recll our LP emple problem we hve been working on, in equlity form, is given below.,,,, 8 m F which, when written in slightly different form, is 8 F Recll tht we
More informationDefinite integral. Mathematics FRDIS MENDELU. Simona Fišnarová (Mendel University) Definite integral MENDELU 1 / 30
Definite integrl Mthemtics FRDIS MENDELU Simon Fišnrová (Mendel University) Definite integrl MENDELU / Motivtion - re under curve Suppose, for simplicity, tht y = f(x) is nonnegtive nd continuous function
More informationPlaying Games with Timed Games,
Plying Gmes with Timed Gmes, Thoms Chtin Alexndre Dvid Kim G. Lrsen LSV, ENS Cchn, CNRS, Frnce (emil: chtin@lsv.ens-cchn.fr) Deprtment of Computer Science, Alborg University, Denmrk (emil: {kgl,dvid}@cs.u.dk)
More informationA Tracking Semantics for CSP
A Trcking Semntics for CSP Mris Llorens, Jvier Oliver, Josep Silv, nd Slvdor Tmrit Universidd Politécnic de Vlenci, Cmino de Ver S/N, E-46022 Vlenci, Spin {mllorens,fjoliver,jsilv,stmrit}@dsic.upv.es Abstrct.
More information