Verification of telecommunication protocols based on formal methods

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1 Internationa Journa of Inteigent Information Systems 01; (1) : 1-10 Pubished onine February 0, 01 ( doi: /j. ijiis Verification of teecommunication protocos based on forma methods Tkacheva Eena Borisovna, Lubov Demchenko Vasiievna, Saied Haawa Fawaz Kharkiv Nationa University of Radio and Eectronics, Kharkov, Ukraine Emai address: korov4enko@mai.ru (T. E. Borisovna), gadiy_v@mai.ru (L. D. Vasiievna), saied.f.h@hotmai.com (S. H. Fawaz) To cite this artice: Tkacheva Eena Borisovna, Lubov Demchenko Vasiievna, Saied Haawa Fawaz. Verification of Teecommunication Protocos Based on Forma Methods, Internationa Journa of Inteigent Information Systems. Vo., No. 1, 01, pp doi: /j.ijiis Abstract: This artice is devoted to the deveopment method for verification and detecting errors that can occur in the operation of protocos for information exchange. The various steps of verification of teecommunication protocos are given in the artice; the construction of counterexampe, which heps to identify the ogica operations that ead to errors in the protocos. Practica impementation of given method is shown on TCP. Keywords: Verification, Mode Checking, E-nets, Forma Grammars, Impementation Mode, Specification Mode 1. Introduction Expansion of services set that are provided by info communication technoogies and aso the progress of information technoogies eads to the necessary to deveop new network protocos or improve existing ones. Now network protocos have a constant growth in the sphere of requirements of protocos reiabiity and a ist of provided services from users, and increasing of requirements to the time for protocos reaization that are impemented by new services from the side of companies at the same time. Thus, the contradiction between requirements and opportunities of design toos, deveopment and depoyment of protocos is increasing a time. As researches show [1, ] the argest number of errors occur at the stage of gathering requirements and forming protocos specification. Typicay, the protocos specifications are defined by a subset of natura anguage. The impementation of the protoco in accordance with these specifications may cause an ambiguous misunderstanding of the requirements, which eads to inconsistent work of protocos eements or various versions of one protoco. One of methods of eimination this probem is the forma presentation of the specification. Verification is one of the methods that aow determining existence errors in the protoco or service. The existing methods of protocos testing have their advantages and disadvantages. In case of appying testing and simuation it is impossibe to assess the correctness of protoco behavior in a situations, they ony can determine the presence or absence of an error according to a certain scenario. In case of teecommunication protocos verification, the most widey used method is Mode Checking method. This method described in [, 4]. It aows to track the whoe set of possibe states of the protoco that can identify nonstandard errors. This method aso aows constructing a counterexampe that is a variant of the protoco behavior, in which the error can be corrected. However, this method has a significant disadvantage combinatoria exposion effect of the state space that in the case of verification of compex teecommunication protocos makes it impossibe to use. Thus there is a need to deveop a new forma method for verification of teecommunication protocos, which aows eiminating the effect of the combinatoria exposion. In this paper, we describe the steps and forma methods (forma specification, anaysis and verification) which hep to detect errors during the whoe ife cyce of protoco. The primary contributions of this paper are: Tempora ogics demonstration (Leaner Tempora Logic, LTL and Computationa Tree Logic, CTL) which aow describing the consecutive change of the state transitions. Demonstration modified method for verification which is based on Mode Checking and use E-nets as instrument for protoco modeing. Aso this method used forma grammas for deeper verification and reduction of the combinatoria exposion (demonstrated in Fig. ). Demonstrating the steps of formuation transition firing in E-nets (consider different types of transitions). The deveoped method of comparing of forma grammar is

2 Tkacheva Eena Borisovna et a.: Verification of teecommunication protocos based on forma methods based on comparison of anguages that describes the behavior of the impementation mode and specification mode of teecommunication protoco. Figure. A modified method of Mode checking for verifying teecommunication protocos.. Steps of Detecting Errors on Logic Operation of Teecommunication Protocos.1. Forma Specification The specific of the protocos is that they have a significant number of parae processes which can potentiay interact at any time. Goba properties of parae processes often cannot be formuated in terms of the reationship between inputs and outputs. Tempora ogics are appied to faciitate the forma specification of such properties. Tempora ogics aow formuating protoco requirements and describing their basic properties, in sequences of performed events and support the formuation of the protoco behavior changes at any time [5]. The set of requirements, which are submitted by the specification, is defined by the set of atomic utterances. Tempora ogics aso compemented by tempora operators, which determine an order and a frequency of event occurrence. Formay, tempora ogic is defined as: TL=<A, O, C>, where A - the aphabet of tempora ogic; O - the set of tempora operators; C - ogica connectives. Formaization of specification s requirements can be represented by two types of formuas: path formuas f = f ( a 1... an) - statements true for the ifetime of the process; state formuas p = P( a1) - statements are true for a certain state of protoco [6, 7]. Path formuas are buit from tempora operators over the states formuas. The state formuas can be true on one state, and the path formuas during some path. The state formua is a formua of ogic anguage of predicates cacuus over some eements of the program s memory state. Path formuas are constructed from the state formuas, ogica and tempora operators. By means of tempora ogics the foowing casses of temporary properties of teecommunication protocos are marked out: Liveiness a property indicating that the protoco wi periodicay go to the desired state; Security a property indicating that the protoco is not prone to erratic behavior; Correctness during execution the protoco wi enter the desired state; Often the impementation of the protoco is represented as a mathematica mode (usuay modeing toos are the varieties of automatons) [8]. The traditiona approach of Mode Checking method based on compete search and comparison of eements of tempora ogic formuas and finding their corresponding position in the impementation protoco mode, as we as estabishing appropriate inkages between the mode states and eements of tempora ogic formuas. If discrepancies between a protoco impementation (the actua behavior, obtained during a mode functioning) and its specification are found, then a counterexampe is being formed that shows how to eiminate this discrepancy. In Fig. 1 it is shown the traditiona scheme of the Mode Checking method. Figure 1. The traditiona scheme of the Mode Checking... The Modification of the Mode Checking Method The appication of mode checking method can be divided into the foowing steps [, 4]: 1. Buiding of mathematica mode of the anayzed system and mode specification.. The formaization of the protoco behavior on the basis of the buit mode.. Presentation of a forma proof of the presence or absence of the specified property in the system. Within the bounds of the genera probem of deveoping methods for the communication protocos anaysis at the stage of requirements forming, specification and impementation of the protoco the E-nets are seected as a means of modeing [8]. Formay E-network is defined as a bipartite directed

3 Internationa Journa of Inteigent Information Systems 01 1(1): 1-10 graph: E = ( P, H, L, D, A, M0), where P is a finite set of paces, H is a finite set of transitions, Lis a direct function of incidence, D is the inverse function of incidence A is a finite set of transition feature set, M 0 is initiaizes the network. Thus, the impementation and specification mode, represented as E-net mode, is the input data for the method of verification which is being deveoped...1. Appication of Forma Grammars. Verification on The Basis of Forma Grammars Forma grammars aow describing the protoco behavior in the form of anguage words. Word is a state of protoco (according to specification and impementation mode), which describe a sequence of protoco state transitions. Thus, the probem of communication protocos verification is reduced to the probem of checking the equivaence of two anguages that are based on forma grammars describing their behavior. Using this method aows to avoid the effect of combinatoria exposion of the state space as comparison of two forma grammars is based on sequentia checking of equivaence of chains of the anguages which describe the specification and impementation of the protoco. The method of verification based on forma grammar consists in foowing [9-11]. The set of possibe behaviors (the chains of anguage) of impementation and specification mode of the protoco is defined by the set of transitions which define the aphabet of forma grammar (Σ). For the specification mode the initia state s 0 is defined, which corresponds to the initia statement of tempora ogic formua that is true in a given s = ϕ state ( 0 ). The fina state of the impementation and specification mode of the protoco (F ) is a key state which must be achieved during functioning of the protoco. It is suggested to use the foowing modification of the Mode Checking method depicted in Fig.. The anguage is formed from the set of transitions that have been aunched during the states transition of the protoco mode. For soving the probem of checking the equivaence of the two anguages which are generated by a forma grammar, it is necessary to introduce a few statements and definitions. During checking the equivaence of specification and impementation of the protoco, the foowing situations can occur: 1. For the specification mode ony one behaviora chain is buit:... Rues for Construction of Forma Grammar for Different Type of Transition in E-Nets T-transition modes the execution of the event, when coming ony one condition. To fire T-transition to the ack of abe in the output position p ( B) = 0 and the presence of the abe in the input positionp ( A) = 1. The exampe of T-transation is present in Fig.. Figure. The structure of T-transition. Rue of inference for T-transition has the next form: L ( T) = { ut T tv} = { utv}, T} N,{ u, v, t} V. { t F- Transition is used for branching fow conditions or branching fow of transmitted data. For fire of F-transaction needed the ack of abe in position p ( B) = 0 and p ( C) = 0, and existing abe in input positionp ( A) = 1. The exampe of T-transition is present in Fig. 4. Figure 4. The structure of F-transition. Branching fow can be expressed as the formaism: L ( F) = { uf F fzv} = { ufzv}, F} N,{ u, z, v,f} V. { t J- transition is used to simuate events that require two conditions at the same time. J-transition is active, ony in one case, when both position А and В contains a abe, p ( A) = 1 and p ( B) = 1 and position С doesn t incude abe, p ( C) = 0 (Fig. 5). L ( S) = ( S0h1... hz ) (1) Where S 0 is the initia state of the mode, which is determined by marking of E-net, h 1...hZ is the set of active transitions of the mode, L (S) is the behavior anguage of the mode. Figure 5. The structure of J-transition. Inference rues for the J-transition have the form:

4 4 Tkacheva Eena Borisovna et a.: Verification of teecommunication protocos based on forma methods L ( J) = { vvj J jz} L( J) = { uvjz}, { J } N,{ u, v, z, j}. V t On Fig. 8 shown a fragment of E-net, which specifies one behaviora chain (one variant). MX- transition sets the direction of abes fow which depending on the vaue of the predicate r (S) (Fig. 6). Figure 6. The structure of MX-transition. Chaining is as foows: or Where usx ( u X, S x X z) L( MX ) = r( S) = 0 ( p( C) = 0) uxv L( MX ) = { uxv} usx ( u X, S x X a) ( ) = r( S) = 1 p(b) = 0) uxz ' L MX ' L( MX) = { uxz} Figure 8. E-net fragment which corresponds a one variant of state transition. The initia state is P 1. The fina state is P 5. This anguage is finite and does not contain cyces. Language that describes the behavior of the given fragment of E-net can be represented as foows: L ( S ) = ( P1h1h h ) () { S, X} N,{ C, B, u, v, z, x} MY- transition is used to mode the priority processing of different streams abes (Fig. 7). V t. Behaviora chain corresponds to severa independent sequences of states transition: L ( S ) = ( S 0h1... S 0h i hz ) () In Fig. 9 it is shown a fragment of the E-net, for which a few chains may appear. There is a possibiity of deadock formation (transitionh 4 ) in such network. A possibe scenarios of mode behavior depending on the conditions of triggering of the transition h 1 are foowing. Figure 7. The structure of MY-transition. Chaining is as foows: u yv, ys, yy, z LMY ( ) 0 ( ( ) 1, ( ) 1, ( ) 0) ( ) uvsy rs = pb = pa = pc = uyz = u yv, ys, yy, z rs ( ) = 1 ( pb ( ) = 1, pa ( ) = 1, pc ( ) = 0) vyz LMY ( ) = { uyz vyz} Where { S, Y} N,{ A, BC,, u, y, v,z} V t On the basis of the rues of inference of productions for standard types of transitions E-nets formed method parse the entire mode of the protoco.... Checking te Equivaence o te Two Languages, Generated by a Forma Grammar Figure 9. The E-net fragment that corresponds to severa independent sequences of states transitions. The initia state is P 1, the fina state is P 9. Language

5 Internationa Journa of Inteigent Information Systems 01 1(1): that describes the behavior of the given fragment of E-net can be represented as foows: L( S ) = ( P1h1h h6h7 P1h P1h 5 P1h h5h4h' 7 ) (4) Moreover, the chain P 1 h eads to the appearance of a deadock in the state P 6 if the transition h 5 is not active or vice versa: the chain P 1 h 5 eads to the appearance of a deadock in the state P 7 if the transition h is not active. The transition h 4 is considered to be ive (active), if each input position has at east one token. There are parae processes interacting with each other (they correspond to the formation of cyces): m ( 0 1 i j Z L S) = ( S hh...( h...) h ). (5) A fragment of the E-net with the possibiity of intereave chain has a structure shown in Fig. 10. Figure 10. E-net fragment which corresponds to the formation of cyces. The presence of intereaved chains can indicate the formation of oops. Verification of the modes in which may appear the oop is the most difficut task. The probem is soved by an additiona method of checking agorithm of doube Depth-First Search (DFS) [1]. If intereaved m chains L S) = ( S hh...( h...) h ) appear during buiding ( 0 1 i j Z of anguage modes, then quantitative assessment of a correspondence between the aunch of transition in specification and impementation modes. Quantitative ratio can be set by using an additiona counter t; it corresponds to the degree of transitions in the mode specification anguage. In this situation, attributes of predicates have the foowing meaning: if the number of tokens that hit the positionp 4 greater than, they wi be dropped, and if it is ess than, then the tokens need to hit the position P again. Language that describes the behavior of the fragment of E-net (Fig. 10) is represented as foows n = P1h1h P1h1 hh 4 (6) L( S ) h Thus, the output of the second chain shows that the number of transition activation h does not affect the aunch of other transitions, and activation of transition h is aowed ony three times. Ony in this case, based on the definitions and, the chain is aowed. For each of the transitions the counter t has its own vaue: n h1 t =, h t = n, h t =, h4 t =. (7) Using the definitions and statements above, and considering exampes of the graph topoogy of E-nets a method of comparison of the two anguages can be formuated. It describes the dynamics of the specification and impementation mode behavior of teecommunications protocos: 1. Buiding a protoco specification anguage L ( MS). L( MS) = ( S0γ γ F), where γ - singe chain or a set of chains which are generated from the initia state.. Performing a step-by-step buiding of a protoco impementation anguage: - determining the current state of the protoco impementation mode (in the first step the current state is the initia S 0( MR) ); - determining the set of active transitions { h M }; - forming a aunch chain for a set of active transitions: h M h M +1.. The comparison of buit anguage chains of protoco impementation mode with active anguage chain of protoco specification mode. hs, True h, i S h i Mi δ( hs 1,, ) ( 1,, ) i Si hs δ h i Mi Mi hmi vi( hs, h ) i M = and i 0, Fase hs h, i Mi δ ( hs 1, S, ) ( 1,, ), i i hs δ h i M M i i h Mi 4. If anguage chains of protoco impementation mode and anguage chains of protoco specification mode are equa then step is repeated with the changing of current state. Otherwise, the counterexampe wi be buid... Deveopment of a Method of Forming Counterexampes The advantage of the suggested method of verification of teecommunication protocos is the abiity to form counterexampes. Counterexampe can determine the protoco behavior, which can ead to an error [1]. For those situations where a formation of severa parae chains L( S) = ( S0h1... S0h i hz ) is possibe, some fragment of the mode is returned as a counterexampe. It incudes an accessibiity chain v and the foowers of the ast matched transition h M i + 1 (it is enough to indicate ony the first foower), as we as the state, the occurrence of which is not vaid in the given sequence: (8)

6 6 Tkacheva Eena Borisovna et a.: Verification of teecommunication protocos based on forma methods L( K) = vh M + 1 ( sm = ψ) i (9) To prevent the oops formation in permissive sequences and to check emptiness of protoco impementation mode anguage L (M) the agorithm of doube Depth-First Search [1] is used. This agorithm is designed to find the permissive paths both in specification and impementation modes of a protoco and is used by many verifiers, incuding SPIN verifier and Bogor [14, 15]. In this agorithm, two depth-first searches are interchanged. The first of them can run the second one and the second, in its turn, can either compete the entire agorithm or return contro to the first DFS. In this case, the first DFS continues its work. Each DFS uses its own fag to mark the visited states. The first DFS aunches the second one when it is ready to ro back from permissive state ( h j ). If during bypassing the second depth-first search enters into the state which is contained in the first DFS stack, then permissive path is obtained. If not, then after terminating bypass the second depth-first search returns contro to the first. Agorithm returns true, if permissive path was found, and fase otherwise. If the agorithm returns true, then it can recover permissive path: in the first DFS stack the path from the initia state h i to some permissive state h j is stored. This path is the required suffix β. The second DFS stack stores the path from the state h i or the initia state of the mode to the state h j which is contained in the first DFS stack. Then, to compete this path by states that are in the first DFS stack before the state h j, we get a cyce hi... hj... hi that passes through a permissive state h i, which is the required suffix β. Thus, the permissive path wi be obtained: L ( K) = vβ (10) DFS agorithm finds a sequence that is aowed by the E-net if and ony if it exists. If the sequence does not exist, the answer fase is returned, which may indicate a ack of active transitions in the protoco impementation mode. If the ast matching symbo of impementation mode does not have any foowers, i.e. the state which is determined by the specification does not exist, fase wi be returned as a counterexampe and the sequence wi be as foows: L ( K) =v Ø (11) It shoud be mentioned that a discrepancies are being searched for each anguage chain separatey. Ony after a the chains of the specification mode are compared to the chains of impementation mode, a fina verification resut with a positive response (conformance of protoco impementation to its specification) or a counterexampe wi be returned.. Resuts As exampe we concede the process of verification for TCP protocos (connection is estabished), with use to different operation systems [10, 16]. Mode of the connection protoco TCP, showing the desired behavior that is based on the unit E-nets is as foows (Fig. 11 and Fig. 1). Figure 11. Specification mode for connection process, buit on the basis of unit E- net.

7 Internationa Journa of Inteigent Information Systems 01 1(1): The state Cosed corresponds initia stage of estabish connection, Listen corresponds to the opening of the port to isten for TCP connection requests, SIN send corresponds to the fact of the communication with the fag of the SIN of the device (passive connection), SIN send corresponds to the formation request SIN device (active compound), SIN received corresponds to receiving a message SYN, SIN not received - SYN message is received, Send ACK, SYN +1 - buid message ACK (repy message SYN); Not generate ACK - the device does not respond, cannot buid message ACK, ACK received - match en receiving a message ACK, ACK not received - ACK message is not received, Estabished - session is set. The first step is to estabish the verification of the initia state ( s 0 ) corresponding with the initia markup mode ( M 0 ), which corresponds to the foowing markup M 0 =(1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0). The initia state is the state of Cosed. Ony active transition is h 1. The fina state is estabished, which is a no termina symbo. Compete description of the protoco behavior scenarios can be represented by the foowing chain of anguages: h1 h1hact h1hacthact h1hacthacth4act h1hacthacth9 act ( r( x) ) Figure 1. Impementation mode for connection estabishment, buit on the basis of the E-machine network. As it can be seen from the sequence at start of transition h act two scenarios are possibe connection, we consider each of them separatey: First scenario: hh h h hh h h h 1 act act 4act 1 act act 4act 5act hh h h h h hh h h h h 1 act act 4act 5act 6act 1 act act 4act 5act 8act ( r( x) ) h1hacthacth9act ( r( x) ) h1hacthacth9act ( r( x) ) hact h1hacthacth9act ( r( x) ) hacthact h1hacthacth9act ( r( x) ) hacthacth4act h1hacthacth9act ( r( x) ) h h h ( r( x) ) act act 9act h1hacthacth9act ( r ( x ) ) h h h h ( r ( x ) ) h 1 act act 9act act h1h acth acth 9act ( r ( x ) ) h acth acth9act ( r ( x ) ) h acthact h1hacthacth9act ( r ( x ) ) h acthacth9act ( r ( x ) ) hact hacthacthact h1hacthacth9act ( r ( x ) ) h acthacth9act ( r ( x ) ) hact hacthacthacth4act h1hacthacth9act ( r ( x ) ) h acthacth9act ( r ( x ) ) hact hacthacthacthacthacth9act ( r ( x ) ) h1 hacthacth9act ( r ( x ) ) Sequence

8 8 Tkacheva Eena Borisovna et a.: Verification of teecommunication protocos based on forma methods h1 h act h acth9 ( r( x) ) act > eads to a dead end, and the rejection of abes (getting into position с ). Starting the transition h 5 act as we as the transition h act gives rise to two possibe scenarios: h1hacthacth4acth5acth 6act, h1hacthacth4acth5acth8 act( r( x) ). Let us consider each scenario separatey. h h h h h h ( r( x) ) 1 act act 4act 5act 8act h h h h h h ( r( x) ) h 1 act act 4act 5act 8act act h h h h h h ( r( x) ) h h 1 act act 4act 5act 8act act act h h h h h h ( r( x) ) 1 act act 4act 5act 8act h h h act act 4act h h h h h h 1 act act 4act 5act 8act act act 9act 1 act act 4act 5act 8act act act 9act 5act 6act 7act act 1 act act 4act 5act 8act act act 9act 5act ( r( x) ) h h h ( r( x) )... h h h h h h ( r( x) ) h h h ( r( x) ) h h h h h h h h h h ( r( x) ) h h h ( r( x) ) h h 6 act. Sequence eads to the rejection of abes (getting into position с) But h1hacth acth4acth5acth8act ( r( x) ) > hh h h h h ( r( x) ) h h h ( r( x) ) h h h h 1 act act 4act 5act 8act act act 9act 5act 6act 7act act to the stage of the connection: h1hacthacth4acth5acth8act ( r( x) ) hacthact h ( r( x) ) h h h h ( Estabished ) Open 9act 5act 6act 7act act h1hacthacth4acth5acth6act h1hacthacth4acth5acth6acth7act h1hacthacth4acth5acth6acth7acth h1hacthacth4acth5acth6acth7acth10act ( r( x) ); h1hacthacth4acth5acth6acth7acth h1hacthacth4acth5acth6acth7acth ; ( Estabished ) Open Thus, for the mode specification condition active open connections meet the foowing scenarios presented by the anguage of P-type: Where Estabishe d - fina state; Cosed initia state. On the basis of the constructed anguage of P-type, there are seven basic scenarios connectioness protoco TCP (active open), which incude the possibiity of accounting retry imit in accordance with the specification. However, there is the possibiity of a third-party request for the estabishment of the session in the position SIN send ( p ), in this situation vaue of the initia marking is M 0 =(1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0). L( P) = Cosed hh 1 acthacth4acth5acth6act h h ( Estabished ) Open 7act 1( act act 9act( ( ) )) h5acth6acth7acth h h h h r x ( Estabished ) Open h1( hacthacth9act( r( x) )) h5acth8act( r( x) ) h h h ( Estabished ) Open 6act 7act h1( hacthacth9act( r( x) )) h5acth8act( r( x) ) h6acth7acth10act ( r( x) ) h ( Estabished ) Open 1( act act 4act 5act 8act( ( ) )) h6act h h h h h h r x h h ( r( x) ) h ( Estabished ) Open 7act 10act h1( hacthacth4acth acth act( r( x) )) h h h ( Estabished ) Open 7act 5 8 6act (11) In this case the behavior of the protoco under the connection can be represented by the foowing chain: Cosed h h ' ( h h ' ) h h pas pas ( h h ' ) h h h ( h h ' ) 1 1 pas pas 4 pas 1 1 h h h pas pas 6 pas 1 1 pas pas 4 pas 1 1 pas pas 4 pas ( r( x) ), ( h h ' ) h h h ( h h ' ) h h h h 5 pas ( h h ' ) h h h h ( r( x) ), 1 1 pas pas 4 pas 7 pas ( h h ' ) h h h h 1 1 p a s p a s 4 p a s ( h h ' ) h h h h 1 1 p a s p a s 4 p a s ( E s ta b is h e d ) O p e n 1 1 pas pas 6 pas ( h h ' ) h h h ( r( x) ) ( h h ' ) h h h ( r( x) ) h 1 1 pas pas 6 pas pas ( h h ' ) h h h 1 1 pas pas 6 pas ( r ( x) ) h h pas pas ( h h ' ) h h h 1 1 pas pas 6 pas ( r ( x) ) h h h pas pas pas 4 pas ( h h ' ) h h h 1 1 pas pas 6 pas ( r ( x) ) h h h h pas 4 pas 6 pas ( r ( x) ) ( h1 h ' 1) h pash pash6 pas ( r ( x) ) h4 pas, hh h h h h h h ( r( x) ) hh h h h h h h ( r( x) ) h * 1 act act 4act 5act 6act 7act 10act 1 act act 4act 5act 6act 7act 10act Where * is symboizes about possibiity of any of the previous scenarios, r (x) is the number of repeated packages.

9 Internationa Journa of Inteigent Information Systems 01 1(1): ( h h ' ) h h h h ( r( x) ) 1 1 pas pas 4 pas 1 1 pas pas 4 pas 7 pas ( h h ' ) h h h h h 5 pas 7 pas ( r( x) ) ( h1 h ' 1) h pashpash4 pash7 pas ( r( x) ) ( h h ' ) h h h h 1 1 pas pas 4 pas 6 pas ( r( x) ) h h h h pas pas 4 pas ( h h ' ) h 1 1 ( r( x) ) h pas 4 pas 5 pas pas pas 4 pas 6 pas pas h h h h pas pas 4 pas 5 pas 7 pas h h h h h h h 5 pas ( r( x) ) Provided passive opening match foowing behaviora chain presented by the anguage of P-type: L ( P ) = C osed ( h ' 1 h1 ) h h h h p a s p a s 4 p a s ( E sta bish ed ) O p en ( h ' h ) h h h 1 1 p a s p a s 6 p a s ( r ( x ) ) ( h h ) h h p a s p a s 4 p a s ( E sta bish ed ) O p en ( h ' h ) h h h 1 1 p a s p a s ( r ( x ) ) h p a s h h h p a s 4 p a s ( E sta bish ed ) O p en ( h ' h ) h h h 1 1 p a s p a s 6 p as ( r ( x ) ) ( h h ) h 7 p a s p a s p a s 4 p a s 7 p a s p a s p as ( 4 p a s ) h h h h h ( E sta b ish ed ) O p en ; (1) Consider a mode of the TCP connection to Unix-ike systems (Fig. 11). According to the method of checking the equivaence given in (8), step through the construction of the anguage impementation of the protoco, to form a anguage according to the rues of grammar for the initia state is determined by the impementation mode. In the framework of our impementation of the protoco TCP two connection option investigate: passive open and active open. Initiaizes the active connection is opened M 0 =(1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0) passive open is possibe at the initia marking M 0 = (1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0). In the case of an active open ony one active transition presentsh 1, Cosed h 1. In passive opening typica transition activity h 1 andh ' 1, Cosed ( h ' 1 h1 ). Perhaps the formation of severa parae chains L( S) = ( S0h1... S0h i hz ) as a counterexampe given fragment of the mode, which incudes a chain of reach abiity v and ast matched transition h : L( K) vh M 1 ( s = ψ) +1 M i = i + M In the process of checking equivaence of anguages that describe the behavior of protoco impementation and specifications modes, found the foowing matching chain: v1 = Cosed h h h h h h h h ( Estabished ) Open v = Cosed ( h ' h ) h h h h 1 act act 4act 5act 6act 7act (1); 1 1 pas pas 4 pas 5 pas (14); ( Estabished ) O pen v = Cosed h1( hacthacth9act ( r( x) )) h5act h6acth7acth ( Estabished ) Open v4 = Cosed ( h ' h ) h h h ( r ( x) ) 1 1 pas pas 6 pas ( h ) pash pas h4 pas h5 pas ( Estabished ) Open As a counterexampe, the foowing chain: L( K ) 1 = Cosed hh h h h h 1 act act 4act 5act 8act L( K ) = Cosed h h h h h h h h 1 act act 4act 5act 6act 7act 8act ( h' 1 h1) hpashpash6pas (15); (16). ; (17) ; (18) L( K ) = Cosed ; (19) L( K ) = Cosed. (0) 4 ( h ' 1 h1) h pashpash4 pash6pas Obtained counterexampes (17-0) indicate that transitions h 8 act and h 6 pas in the impementation of the protoco does not correspond to requirements of the specification. According to agorithm DFS, for transition firing h 8 act requires abes in positions p 11 andp 1, that it is impossibe. Labes in positions p 5 andp 7 requires for the firing transitionh 6 pas, but that it is impossibe in impementation mode too. Thus, this method of comparison chains anguage modes can verify the equivaence of the behavior of the specification and impementation of the protoco. 4. Concusion In the artice suggested a modified method for verification and detecting the errors that arise in the operation of protocos for information exchange. This method is based on Mode Checking method for verifying teecommunication protocos and additionay used the forma grammars to show possibe soutions for resoving the issue. The use of forma grammars aso heps to avoid combinatoria exposion effect of the state space which constructs the impementation and the specification modes.

10 10 Tkacheva Eena Borisovna et a.: Verification of teecommunication protocos based on forma methods This effect is achieved through the impementation of sequentia equivaence checking chains anguages, modes describing the behavior specification and impementation of the protoco. The mode specification and impementation protoco, which buit using the apparatus E-net, are as input data verification method. Presentation protoco by E-mode heps to buid one chain behavior of the protoco. The main advantage of this method compared to the known, is to avoid conficts between the impementation and specification of the protoco by constructing a counterexampe. To check the efficiency of the deveoped verification method for equaity of anguages buit on the basis of the rues of forma grammar for suggested verification protoco on TCP with its impementation in Unix systems on estabishing connection stage. References [1] ISO/IEC 1410:008. Information technoogy - Guideine for the evauation and seection of CASE Toos, 008. [] The Standish Group. The Scope of Software Deveopment Project Faiures: The Standish Group. Stanford, 009, [] Jr. Carke, M. Edmund, and A. Peed, Mode Checking, MIT Press, 1999, ISBN [4] B. Berard, M. Bidoit, A. Finke, F. Laroussinie, A. Petit, L. Petrucci, and P. Schnoebeen, Systems and Software Verification: Mode-Checking Techniques and Toos, 009. ISBN [5] C. P. Stiring, Moda and tempora ogics for processes. LNCS 104, 1996, pp [6] J. Bradfied, C. Stiring, Moda ogics and mu-cacui, Inf.ed.ac.uk [7] G Nutt, Evauation Nets for Computer Systems Performance Anaysis. FJCC, AFIPSPRESS. 197, pp [8] A. Mironov, A new method of verification of protocos of data transmission through unreiabe medium, Summer Schoo in Software Engineering and Verification, Moscow, 011, pp [9] N. Chomsky, "Three Modes for the Description of Language". IRE Transactions on Information Theory (). 1956, pp doi: /tit [10] E. Korovchenko, Modes and methods for anaysis and verification teecommunications protocos based on the E-networks and forma grammars, Master s thesis, Kharkov nationa University of Radio eectronics, Oct [11] E. Duravkin, E. Korovchenko, The formaization of the information exchange protocos behavior provided by modes based on E-network, the probems of teecommunication (e-journa). vo. 1 (). pp. 8 8, 011: df. [1] A.T.S. Abu-Jassar, O. Tkachova, Patterns for reiabe Web-services, The probems of teecommunication (e-journa). vo. (7), pp. 6 4, 01: [1] L. Hoffman, Taking Mode-Checking Technoogy, Communications of the ACM, 008, pp [14] Forma Grammar: 14th Internationa Conference, FG 009, Bordeaux, France, Juy 5-6, 009. [15] J. Poste, Transmission contro protoco. RFC 79, Caifornia, sept. 1981, 85 p. [16] A. Strunk An agorithm to predict the QoS-Reiabiity of service compositions. In: SERVICES, 010, pp