D. Brand and P. Za ropulo. On communicating nite-state machines. Journal of the ACM, 30(2):323-342, 1983.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....al [1, 2] which de ne two notions of realizability: weak realizability and safe realizability. Both are based on the model of communicating nite state machines (CFMs) with FIFO queues for describing the implementation. CFMs appeared as one of the earliest abstract models for concurrent systems [5, 18], and are used for instance in the speci cation language SDL [13] An accepting run of a CFM generates in a canonical way an MSC. Thus, in [2] an HMSC H is called weakly realizable, if there exists a CFM A such that the set of all MSCs generated by the accepting runs of A is precisely the set of ....

D. Brand and P. Za ropulo. On communicating nite-state machines. Journal of the Association for Computing Machinery, 30(2):323-342, 1983.

....behavior, such as corruption and duplication of messages, and insertion of new messages, and show that the decidability results extend to these models. 1 Introduction Finite state machines which communicate through unbounded bu ers have been popular in the modelling of communication protocols [BZ83,Boc78]. One disadvantage with such a model is that it has the full computation power of Turing machines [BZ83] implying undecidability of all nontrivial veri cation problems. On the other hand, many protocols are designed to operate correctly even in the case where the underlying communication medium ....

....results extend to these models. 1 Introduction Finite state machines which communicate through unbounded bu ers have been popular in the modelling of communication protocols [BZ83,Boc78] One disadvantage with such a model is that it has the full computation power of Turing machines [BZ83], implying undecidability of all nontrivial veri cation problems. On the other hand, many protocols are designed to operate correctly even in the case where the underlying communication medium is faulty. To capture the behaviour of such protocols, lossy channel systems (LCS) AJ96b] have been ....

D. Brand and P. Za ropulo. On communicating nite-state machines. Journal of the ACM, 2(5):323-342, April 1983.

....too. Our proof depends upon simulating a perfect channel, with a high degree of con dence, using lossy channels. 1 Introduction Finite state machines which communicate over unbounded FIFO channels have been used as an abstract model of computation for reasoning about communication protocols [4], and Supported in part by ARO under grant DAAG55 98 1 03093 and by STINT. A version of this paper appeared in the proceedings of CONCUR 2000. they form the backbone of ISO protocol speci cation languages Estelle and SDL. However, the model is Turing powerful which makes most veri cation ....

.... . If a computation is nite we say that leads from 1 to n . We de ne the control state reachability problem for CFSMs (Reach CFSM) as follows Instance A CFSM C and a control state s in C. Question Is there a w such that hs; wi is reachable The following result is well known (e.g. [4]) Theorem 2.2 Reach CFSM is undecidable. The idea behind the proof is to use one of the channels to simulate the tape of a Turing machine. In fact, this construction implies that the problem is undecidable even for the class of CFSMs with only one channel. We can make a further restriction on ....

D. Brand and P. Za ropulo. On communicating nite-state machines. Journal of the ACM, 2(5):323-342, April 1983.

....for these systems. In this article we show that these problems cannot be solved in primitive recursive time. 1 Introduction Channel systems, also called Finite State Communicating Machines, are systems of nite state automata that communicate via asynchronous unbounded fo channels [Boc78, BZ83] Figure 1 displays an example, where the labels c x and c x mean that message x (a letter) is sent to (respectively read from) channel c. Channel systems are a natural model for asynchronous q 1 q 2 q 3 c 1 b c 2 c c 2 a c 1 a p 1 p 2 c 1 a c 2 a c 2 c c 1 b channel c 1 b a a b ....

....i ) or (3.2) there is a rule (q; c i ; u; q 0 ) 2 such that w i = uv (u has been read from the head of c i ) These steps are called perfect because no message is lost. It is well known that, assuming perfect steps, channel systems can faithfully simulate Turing machines in quadratic time [BZ83] a single channel is enough to replace a Turing machine work tape; reading and writing in the middle of the channel requires rotating the content of the channel for positioning reasons, hence the quadratic overhead) Thus all interesting veri cation problems are undecidable for systems with ....

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D. Brand and P. Zaropulo. On communicating nite-state machines. Journal of the ACM, 30(2):323-342, 1983.

....assumes that messages can be lost while they are in transit, without any noti cation. Protocol designers know that unreliable channels are very real but, because they know how to cope with unreliability (e.g. with the alternating bit protocol) the classical model assumed perfect channels [Boc78,BZ81] Therefore it is really ironic, and somewhat paradoxical, that lossy channels are easier to analyze than perfect ones , quoting [CFP95] Finkel showed that termination is decidable for lossy systems [Fin94] Abdulla and Jonsson showed the decidability of reachability, safety properties over ....

....unlabeled S, we sometimes omit writing in S and in the rules. 3. 2 Undecidability of reachability Extended channel systems have undecidable reachability problems for two reasons: 1) standard rules can be used to simulate the tape of a Turing machine on a single fo channel as soon as j j 2 [BZ81, p. 31] and (2) extended rules allow one to simulate a Turing machine on a 2 counters machine [SS63] For our purposes we introduce the following problem, a variant of the halting problem that makes the reduction in section 4 smoother: Non empty Reachability. Instance: An extended channel ....

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D. Brand and P. Zaropulo. On communicating nite-state machines. Research Report RZ 1053, IBM Zurich Research Lab., June

....number of stored occurrences. Related work. The behavioral model for Electre programs [CR95] is close to Communicating Finite State Machines (CFSMs) or Fifo Automata. However, this class has the power of Turing Machines since it s possible to simulate any Turing Machine by a system of two CFSMs [BZ83,FM97]. The reachability problem is decidable for systems with the recognizable channel property [Pac87] but this result cannot be easily used in general because this property is undecidable. Decidability results have been established for particular classes of Fifo Automata. The reachability problem is ....

D. Brand and P. Zaropulo. On communicating nite-state machines. JACM, 30(2):323342, 1983.

....we use are: a) the reachability set of a ring network which at least one queue is a counter is constructively recognizable; b) the reachability problem is decidable for ring networks with at least one lossy queue. 1 Introduction The communicating nite state machines model is Turing powerful [BZ83]. So the rst approach to study this model was the search for decidable subclasses. However, in addition to be constraining, a major disadvantage of this approach is the impossibility, in general, to know whether a given system belongs to one of those subclasses. Therefore, this rst approach is of ....

....i=1 W i;1 Theta : Theta W i;p 5 3 Generalization of 1 Counter Automata By relation (2) in previous section, computation of the reachability set of a queue automaton A is reduced to computation of A(q o ; q) for all control state q . Since A(q o ; q) is not computable in general [BZ83], we shall compute a sequence fW i g i=1; n such that W o = f g and W i 1 is a recognizable approximation of A(q i ; q i 1 ) W i ] with q i 2 Q and q n = q . By doing this, W n approximates A(q o ; q) And the better the intermediate approximations W i are, the better W n is. So, given ....

D. Brand and P. Zaropulo. On communicating nite-state machines. JACM, 30(2):323342, April 1983.

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D. Brand and P. Za ropulo. On communicating nite-state machines. Journal of the ACM, 30(2):323-342, 1983.

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D. Brand and P. Za ropulo. On communicating nite-state machines. Journal of the ACM, 30(2):323-342, 1983.

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