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Towards a model-checker for counter systems
- In ATVA 2006, 4 th International Symposium on Automated Technology for Verification and Analysis, Beijing, Rep. of China, volume 4218 of Lecture Notes in Computer Science
, 2006
"... Abstract. This paper deals with model-checking of fragments and extensions of CTL * on infinite-state Presburger counter systems, where the states are vectors of integers and the transitions are determined by means of relations definable within Presburger arithmetic. We have identified a natural cla ..."
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Cited by 17 (9 self)
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Abstract. This paper deals with model-checking of fragments and extensions of CTL * on infinite-state Presburger counter systems, where the states are vectors of integers and the transitions are determined by means of relations definable within Presburger arithmetic. We have identified a natural class of admissible counter systems (ACS) for which we show that the quantification over paths in CTL * can be simulated by quantification over tuples of natural numbers, eventually allowing translation of the whole Presburger-CTL * into Presburger arithmetic, thereby enabling effective model checking. We have provided evidence that our results are close to optimal with respect to the class of counter systems described above. Finally, we design a complete semi-algorithm to verify first-order LTL properties over trace-flattable counter systems, extending the previous underlying FAST semi-algorithm to verify reachability questions over flattable counter systems. 1
Composability of infinite-state activity automata
, 2004
"... Abstract. Let be a class of (possibly nondeterministic) language acceptors with a oneway input tape. A system of automata in, is composable if for every string of symbols accepted by, there is an assignment of each symbol in to one of the ’s such that if is the subsequence assigned to, then is accep ..."
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Cited by 14 (3 self)
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Abstract. Let be a class of (possibly nondeterministic) language acceptors with a oneway input tape. A system of automata in, is composable if for every string of symbols accepted by, there is an assignment of each symbol in to one of the ’s such that if is the subsequence assigned to, then is accepted by. For a nonnegative integer, a-lookahead delegator for is a deterministic machine in which, knowing (a) the current states! of and the accessible “local ” information of each machine (e.g., the top of the stack if each machine is a pushdown automaton, whether a counter is zero on nonzero if each machine is a multicounter automaton, etc.), and (b) the lookahead symbols to the right of the current input symbol being processed, can uniquely determine " the to assign the current symbol. Moreover, every string accepted by is also accepted by, i.e., the subsequence of string delegated by to " each is accepted by. Thus,-lookahead delegation is a stronger requirement than composability, since the delegator must be deterministic. A system that is composable may not have a-delegator for any. We look at the decidability of composability and existence of-delegators for various classes of machines. Our results have applications to automated composition of e-services. E-
LTL over integer periodicity constraints
- PROCEEDINGS OF THE 7TH INTERNATIONAL CONFERENCE ON FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATION STRUCTURES (FOSSACS), VOLUME 2987 OF LNCS
, 2004
"... Periodicity constraints are used in many logical formalisms, in fragments of Presburger LTL, in calendar logics, and in logics for access control, to quote a few examples. In the paper, we introduce the logic PLTL mod, an extension of Linear-Time Temporal Logic LTL with past-time operators whose a ..."
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Cited by 12 (4 self)
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Periodicity constraints are used in many logical formalisms, in fragments of Presburger LTL, in calendar logics, and in logics for access control, to quote a few examples. In the paper, we introduce the logic PLTL mod, an extension of Linear-Time Temporal Logic LTL with past-time operators whose atomic formulae are defined from a first-order constraint language dealing with periodicity. Although the underlying constraint language is a fragment of Presburger arithmetic shown to admit a pspace-complete satisfiability problem, we establish that PLTL mod model-checking and satisfiability problems remain in pspace as plain LTL (full Presburger LTL is known to be highly undecidable). This is particularly interesting for dealing with periodicity constraints since the language of PLTL mod has a language more concise than existing languages and the temporalization of our first-order language of periodicity constraints has the same worst case complexity as the underlying constraint language. Finally, we show examples of introduction the quantification in the logical language that provide to PLTL mod, expspacecomplete problems. As another application, we establish that the equivalence problem for extended single-string automata, known to express the equality of time granularities, is pspace-complete by designing a reduction from QBF and by using our results for PLTL mod.
Verification of qualitative Z constraints
"... Abstract. We introduce an LTL-like logic with atomic formulae built over a constraint language interpreting variables in Z. The constraint language includes periodicity constraints, comparison constraints of the form x = y and x < y, it is closed under Boolean operations and it admits a restricte ..."
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Cited by 5 (1 self)
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Abstract. We introduce an LTL-like logic with atomic formulae built over a constraint language interpreting variables in Z. The constraint language includes periodicity constraints, comparison constraints of the form x = y and x < y, it is closed under Boolean operations and it admits a restricted form of existential quantification. This is the largest set of qualitative constraints over Z known so far, shown to admit a decidable LTL extension. Such constraints are those used for instance in calendar formalisms or in abstractions of counter automata by using congruences modulo some power of two. Indeed, various programming languages perform arithmetic operators modulo some integer. We show that the satisfiability and model-checking problems (with respect to an appropriate class of constraint automata) for this logic are decidable in polynomial space improving significantly known results about its strict fragments. As a by-product, LTL model-checking over integral relational automata is proved complete for polynomial space which contrasts with the known undecidability of its CTL counterpart. 1
Real-counter automata and their decision problems
- in: FSTTCS, LNCS 3328
"... Abstract. We introduce real-counter automata, which are two-way finite automata augmented with counters that take real values. In contrast to traditional word automata that accept sequences of symbols, real-counter automata accept real words that are bounded and closed real intervals delimited by a ..."
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Cited by 2 (0 self)
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Abstract. We introduce real-counter automata, which are two-way finite automata augmented with counters that take real values. In contrast to traditional word automata that accept sequences of symbols, real-counter automata accept real words that are bounded and closed real intervals delimited by a finite number of markers. We study the membership and emptiness problems for one-way/twoway real-counter automata as well as those automata further augmented with other unbounded storage devices such as integer-counters and pushdown stacks. 1
Linear Reachability Problems and Minimal Solutions to Linear Diophantine Equation Systems Abstract
"... The linear reachability problem for finite state transition systems is to decide whether there is an execution path in a given finite state transition system such that the counts of labels on the path satisfy a given linear constraint. Using some known results on minimal solutions (in nonnegative in ..."
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The linear reachability problem for finite state transition systems is to decide whether there is an execution path in a given finite state transition system such that the counts of labels on the path satisfy a given linear constraint. Using some known results on minimal solutions (in nonnegative integers) for linear Diophantine equation systems, we present new time complexity bounds for the problem. In contrast to the previously known results, the bounds obtained in this paper are polynomial in the size of the transition system in consideration, when the linear constraint is fixed. The bounds are also used to establish a worst-case time complexity result for the linear reachability problem for timed automata. Key words: Model-checking, timed automata, reachability, linear Diophantine equation systems, minimal solutions 1
Real-Counter Automata and Verification ⋆ (Extended Abstract)
"... Abstract. We introduce real-counter automata, which are two-way finite automata augmented with counters that take real values. In contrast to traditional word automata that accept sequences of symbols, real-counter automata accept real words that are bounded and closed real intervals delimited by a ..."
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Abstract. We introduce real-counter automata, which are two-way finite automata augmented with counters that take real values. In contrast to traditional word automata that accept sequences of symbols, real-counter automata accept real words that are bounded and closed real intervals delimited by a finite number of markers. We study the membership and emptiness problems for one-way/twoway real-counter automata as well as those automata further augmented with other unbounded storage devices such as integer-counters and pushdown stacks. 1
The Effects of Bounding Syntactic Resources on Presburger LTL
"... (Extended Abstract) ∗ We study decidability and complexity issues for fragments of LTL with Presburger constraints by restricting the syntactic resources of the formulae (the class of constraints, the number of variables and the distance between two states for which counters can be compared) while p ..."
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(Extended Abstract) ∗ We study decidability and complexity issues for fragments of LTL with Presburger constraints by restricting the syntactic resources of the formulae (the class of constraints, the number of variables and the distance between two states for which counters can be compared) while preserving the strength of the logical operators. We provide a complete picture refining known results from the literature, in some cases pushing forward the known decidability limits. By way of example, we show that model-checking formulae from LTL with quantifier-free Presburger arithmetic over one-counter automata is only PSPACE-complete. In order to establish the PSPACE upper bound, we show that the nonemptiness problem for Büchi one-counter automata taking values in Z and allowing zero tests and sign tests, is only NLOGSPACE-complete. 1
