O. H. Ibarra, T. Jiang, N. Tran, and H. Wang. New decidability results concerning two-way counter machines. SIAM J. Comput., 24:123--137, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....on non regular languages. Ginsburg shows the decidability of language emptiness, containment, and equivalence for bounded languages, those of the form w 1 , such as a [33] Ibarra et al. extended these results to the general class of languages accepted by two way, one counter machines [48]. Harel and Raz investigated non regular extensions of PDL (Propositional Dynamic Logic) programs, identifying three classes of non regular languages such that PDL extended with any language from one of the classes remains decidable [44] Their characterizations are based partially on the ....

....Timing diagram languages resemble bounded languages, those with form w 1 , where each w i is a word [33] In the case of timing diagrams, each w i represents a time slice. Language containment is decidable for bounded languages, regardless of their position in the Chomsky hierarchy [48]. Unfortunately, this result does not apply directly to timing diagrams. The bounded language correlation captures a single instance of a timing diagram, but it cannot capture the multiple instances allowed by the iterative and invariant semantics. Fortunately, decision procedures for certain ....

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Oscar H. Ibarra, Tao Jiang, Nicholas Tran, and Hui Wang. New decidability results concerning two-way counter machines and applications. In Proceedings of the 20th International Colloquium on Automata, Languages, and Programming (ICALP), 1993. Lecture Notes in Computer Science, 700.

....too powerful. In fact, the emptiness problem is undecidable for twoway automata augmented with reversal bounded counters. In the case when there is only one reversal bounded counter, the emptiness problem is decidable if the machines are deterministic. The nondeterministic case is still open [29]. In practice, augmenting timed automata with other unbounded data structures allows us to study more complex real time applications. For instance, the decidable characterization of PTAs makes it possible to implement a tool verifying recursive real time programs containing finite state variables ....

O. H. Ibarra, T. Jiang, N. Tran and H. Wang, "New decidability results concerning two-way counter machines," SIAM J. Comput., 24 (1995) 123-137 29

....too powerful. In fact, the emptiness problem is undecidable for twoway automata augmented with reversal bounded counters. In the case when there is only one reversal bounded counter, the emptiness problem is decidable if the machines are deterministic. The nondeterministic case is still open [29]. In practice, augmenting timed automata with other unbounded data structures allows us to study more complex real time applications. For instance, the decidable characterization of PTAs makes it possible to implement a tool verifying recursive real time programs containing finite state variables ....

O. H. Ibarra, T. Jiang, N. Tran and H. Wang, "New decidability results concerning two-way counter machines," SIAM J. Comput., 24 (1995) 123-137

....language of M and will be denoted L(M ) Languages accepted by 1 2DCM can be characterized by the number of times the counter changes between incrementing and decrementing while reading the input tape. Denoting this parameter by r, the following results about 1 2DCM(r) are due to Ibarra et al. [8]: Theorem 1 (Ibarra et al. 1993) The emptiness problem for 1 2DCM(r) is decidable for every r 1. S r 1 2DCM(r) is effectively closed under complementation, intersection, and union. The containment and equivalence problems for S r 1 2DCM(r) are decidable. This result indicates ....

Oscar H. Ibarra, Tao Jiang, Nicholas Tran, and Hui Wang. New decidability results concerning two-way counter machines and applications. In Proc. of the 20th International Colloquium on Automata, Languages, and Programming, 1993. Lecture Notes in Computer Science 700.

....form the language of M , denoted L(M ) Languages accepted by 1 2DCM can be characterized by the number of times the counter changes between incrementing and decrementing while reading the input tape. Denoting this parameter by r, the following results about 1 2DCM(r) are due to Ibarra et al. [15]: THEOREM 1. Ibarra et al. 1993) Gamma For every r 1, emptiness is decidable for 1 2DCM(r) Gamma S r 1 2DCM(r) is effectively closed under complementation, intersection, and union. Gamma Containment and equivalence are decidable for S r 1 2DCM(r) By this result, we can use 1 2DCM ....

Oscar H. Ibarra, Tao Jiang, Nicholas Tran, and Hui Wang. New decidability results concerning two-way counter machines and applications. In Proceedings of the 20th International Colloquium on Automata, Languages, and Programming (ICALP), 1993. Lecture Notes in Computer Science, 700.

....In certain cases, given a parametric timed automaton A, we can construct a restricted 1register machine MA that accepts Gamma(A) and thus reduce the emptiness problem for parametric timed automata with two clocks to the emptiness problem for restricted 1 register machines. A recent result in [IJTW93] shows that the emptiness problem is decidable for deterministic restricted 1 register machines. The problem is still open for nondeterministic restricted 1 register machines. ....

O. Ibarra, T. Jiang, N. Tran, and H. Wang. New decidability results concerning twoway counter machines and applications. In Proc. 20th ICALP, LNCS. Springer, 1993. To appear.

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O. H. Ibarra, T. Jiang, N. Tran, and H. Wang. New decidability results concerning two-way counter machines. SIAM J. Comput., 24:123--137, 1995.

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O. H. Ibarra, T. Jiang, N. Tran, and H. Wang. New decidability results concerning two-way counter machines. SIAM J. Comput., 24:123--137, 1995.

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O. H. Ibarra, T. Jiang, N. Tran, and H. Wang. New decidability results concerning two-way counter machines. SIAM J. Comput., 24:123--137, 1995.

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O. H. Ibarra, T. Jiang, N. Tran, and H. Wang. "New decidability results concerning two-way counter machines," SIAM J. Comput., 24(1):123-137, 1995.

....two way input tape (with delimiters) and one reversal bounded counter C but no parameterized constants, such that M accepts empty if and only if M accepts empty. The result follows since the emptiness problem is decidable for deterministic two way machines with one reversal bounded counter [IJTW95]. has input alphabet f1, g (the delimiter is #) M rejects all inputs not of the form #1 #. Corresponding to values ff 1 ; ff n assigned to the parameterized constants, is given input w = #1 #, where i 1 = ff 1 Gamma 1; i 2 = ff 2 Gamma ff 1 Gamma 1; Delta ....

O. H. Ibarra, T. Jiang, N. Tran, and H. Wang, New decidability results concerning two-way counter machines, SIAM J. Comput., 24(1):123--137, 1995.

.... automata augmented with one reversal bounded counter (i.e. the counter alternates between nondecreasing and nonincreasing modes a fixed number of times) operating on bounded languages (i.e. subsets of w k for some nonnull words w1 ; wk ) is decidable, settling an open problem in [11, 12]. The proof is a rather involved reduction to the solution of a special class of Diophantine systems of degree 2 via a class of programs called two phase programs. The result has applications to verification of infinite state systems. 1 Introduction Automata theory tries to answer questions ....

.... is reversal bounded, emptiness is decidable when the machine is deterministic and accepts a bounded language (i.e. a subset of w k for some nonnull words w 1 ; w k ) 10] This result was later shown to hold for the general case when the the input is not over a bounded language [12]. These machines are quite powerful. They can accept fairly complex languages. For example, such a machine can recognize the language consisting of strings of the form 0 i j where i divides j. A question left open in [11, 12] is whether the aforementioned decidability of emptiness holds for ....

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O. H. Ibarra, T. Jiang, N. Tran, and H. Wang. New decidability results concerning two-way counter machines. SIAM J. Comput., 24:123--137, 1995.

....we show that the binary reachability under any one of the three approximations has a 2DCM padding when the machine is deterministic. Specifically, we show that the padded language for binary reachability can be accepted by a deterministic two way counter machine with one reversal bounded counter [19]. The case for nondeterministic generalized discrete timed automata is open. These are good characterizations in the sense that the validity of Presburger formulas can be verified by these machines, and the emptiness problem for such machines is decidable. This allows us to establish, in ....

....problem for 2DCM(c; r) when c 2 and r 1 is undecidable [18] An interesting special case is when c = 1, i.e. there is only one counter. A language is 2DCM recognizable if it can be accepted by a 2DCM(1; r) Theorem 6. The emptiness problem for 2DCM recognizable languages is decidable [19]. It is still open whether Theorem 6 holds for nondeterministic machines. That is, whether the emptiness problem for 2NCM(1,r) which is a nondeterministic r reversal bounded one counter machine with a two way input tape, is decidable. Given a generalized discrete timed automaton A, consider a ....

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O. H. Ibarra, T. Jiang, N. Tran and H. Wang, "New decidability results concerning two-way counter machines," SIAM J. Comput., 24 (1995) 123-137

....We will need the following result from [17] Theorem 1. There is a fixed r such that the emptiness problem for 2DCM(2,r) over bounded languages is undecidable. We will also need the following results. Theorem 2. The emptiness problem is decidable for the following machine classes: a) 2DCM(1) [18], b) 2NCM(1) over a bounded language [8] c) 2NCM(c) over a unary alphabet (i.e. over a bounded language on 1 letter) for every c [18] and (d) finite crossing 2NCM(c) for every c [17, 15] Let Y be a finite set of variables over integers. For all integers a y , with y 2 Y , b and c (with b ....

....languages is undecidable. We will also need the following results. Theorem 2. The emptiness problem is decidable for the following machine classes: a) 2DCM(1) 18] b) 2NCM(1) over a bounded language [8] c) 2NCM(c) over a unary alphabet (i.e. over a bounded language on 1 letter) for every c [18], and (d) finite crossing 2NCM(c) for every c [17, 15] Let Y be a finite set of variables over integers. For all integers a y , with y 2 Y , b and c (with b 0) y2Y a y y c is an atomic linear relation on Y and y2Y a y y b c is a linear congruence on Y . A linear relation on Y is a ....

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O. H. Ibarra, T. Jiang, N. Tran, and H. Wang. New decidability results concerning two-way counter machines. SIAM J. Comput., 24:123--137, 1995.

....two way input tape (with delimiters) and one reversal bounded counter C but no parameterized constants, such that M 0 accepts empty if and only if M accepts empty. The result follows since the emptiness problem is decidable for deterministic two way machines with one reversal bounded counter [14]. M 0 has input alphabet f1, g (the delimiter is #) M 0 rejects all inputs not of the form #1 i 1 1 i 2 1 i n 1 k #. Corresponding to values 1 ; n assigned to the parameterized constants, M 0 is given input w = #1 i 1 1 i 2 1 i n 1 k #, where i ....

O. H. Ibarra, T. Jiang, N. Tran, and H. Wang, New decidability results concerning two-way counter machines, SIAM J. Comput., 24(1):123-137, 1995.

....problem for 2DCM(c; r) when c 2 and r 1 is undecidable [24] An interesting special case is when c = 1, i.e. there is only one counter. A language is 2DCM recognizable if it can be accepted by a 2DCM(1; r) Theorem 7. The emptiness problem for 2DCM recognizable languages is decidable [25]. It is still open whether Theorem 7 holds for nondeterministic machines. That is, whether the emptiness problem for 2NCM(1,r) which is a nondeterministic r reversal bounded one counter machine with a two way input tape, is decidable. Given a generalized discrete timed automaton A, consider a ....

..... Thus, the safety analysis problem is equivalent to testing the emptiness of M , which is decidable from Lemma 1. Remark: Theorem 11 can be strengthened. The class of languages accepted by deterministic two way counter machines with one reversal bounded counter is closed under Boolean operations [25]. It follows that Theorem 11 remains valid even if the sets of configurations P (property) and I (initial condition) are sets accepted by these machines. It is desirable to consider the decidability of the safety analysis problem for generalized discrete timed automata under some special form but ....

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O. H. Ibarra, T. Jiang, N. Tran, and H. Wang, "New decidability results concerning two-way counter machines," SIAM J. Comput., 24 (1995) 123-137

....number of times the input head crosses the boundary between any two adjacent cells of the input tape (including the end markers) is bounded by a given constant. Every finite crossing 2CA can effectively be converted to a (one way) CA [GuI81] However, the nondeterminism is essential here, see [IJTW95]. Therefore, 5 Corollary 4.1. The languages accepted by finite crossing 2CAs are semilinear, and hence their emptiness problem is decidable. In contrast to the undecidability for 2CAs with two reversal bounded counters, the emptiness problem is decidable for deterministic 2CAs when there is ....

....The languages accepted by finite crossing 2CAs are semilinear, and hence their emptiness problem is decidable. In contrast to the undecidability for 2CAs with two reversal bounded counters, the emptiness problem is decidable for deterministic 2CAs when there is only one reversal bounded counter [IJTW95]. These automata can accept fairly complex languages. For example, such an automaton can recognize the language L = f0 k 1 n j k divides ng that is not semilinear. Thus, unlike finite crossing reversalbounded multicounter automata, these automata can accept languages whose Parikh maps are not ....

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O. H. Ibarra, T. Jiang, N. Tran, and H. Wang. New decidability results concerning two-way counter machines. SIAM J. Comput. 24 (1995), 123 -- 137.

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O. H. Ibarra, T. Jiang, N. Tran, and H. Wang. "New decidability results concerning two-way counter machines," SIAM J. Comput., 24(1):123-137, 1995.

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