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Model checking freeze LTL over one-counter automata
, 2008
"... We study complexity issues related to the model-checking problem for LTL with registers (a.k.a. freeze LTL) over one-counter automata. We consider several classes of one-counter automata (mainly deterministic vs. nondeterministic) and several syntactic fragments (restriction on the number of regist ..."
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We study complexity issues related to the model-checking problem for LTL with registers (a.k.a. freeze LTL) over one-counter automata. We consider several classes of one-counter automata (mainly deterministic vs. nondeterministic) and several syntactic fragments (restriction on the number of registers and on the use of propositional variables for control locations). The logic has the ability to store a counter value and to test it later against the current counter value. By introducing a non-trivial abstraction on counter values, we show that model checking LTL with registers over deterministic one-counter automata is PSPACEcomplete with infinite accepting runs. By constrast, we prove that model checking LTL with registers over nondeterministic one-counter automata is Σ 1 1-complete [resp. Σ 0 1-complete] in the infinitary [resp. finitary] case even if only one register is used and with no propositional variable. This makes a difference with the facts that several verification problems for one-counter automata are known to be decidable with relatively low complexity, and that finitary satisfiability for LTL with a unique register is decidable. Our results pave the way for model-checking LTL with registers over other classes of operational models, such as reversal-bounded counter machines and deterministic pushdown systems.
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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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-
Reversal-bounded counter machines revisited
, 2008
"... We extend the class of reversal-bounded counter machines by authorizing a finite number of alternations between increasing and decreasing mode over a given bound. We prove that extended reversal-bounded counter machines also have effective semi-linear reachability sets. We also prove that the prop ..."
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Cited by 10 (3 self)
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We extend the class of reversal-bounded counter machines by authorizing a finite number of alternations between increasing and decreasing mode over a given bound. We prove that extended reversal-bounded counter machines also have effective semi-linear reachability sets. We also prove that the property of being reversal-bounded is undecidable in general even when we fix the bound, whereas this problem becomes decidable when considering Vector Addition System with States.
On Selective Unboundedness of VASS
, 2013
"... Numerous properties of vector addition systems with states amount to checking the (un)boundedness of some selective feature (e.g., number of reversals, counter values, run lengths). Some of these features can be checked in exponential space by using Rackoff’s proof or its variants, combined with Sav ..."
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Cited by 7 (1 self)
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Numerous properties of vector addition systems with states amount to checking the (un)boundedness of some selective feature (e.g., number of reversals, counter values, run lengths). Some of these features can be checked in exponential space by using Rackoff’s proof or its variants, combined with Savitch’s Theorem. However, the question is still open for many others, e.g., regularity detection problem and reversal-boundedness detection problem. In the paper, we introduce the class of generalized unboundedness properties that can be verified in exponential space by extending Rackoff’s technique, sometimes in an unorthodox way. We obtain new optimal upper bounds, for example for place boundedness problem, reversal-boundedness detection (several variants are present in the paper), strong promptness detection problem and regularity detection. Our analysis is sufficiently refined so as to obtain a polynomial-space bound when the dimension is fixed.
Algorithmic metatheorems for decidable LTL model checking over infinite systems
"... By algorithmic metatheorems for a model checking problem P over infinite-state systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a large family of classes of infinite systems. Such results n ..."
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By algorithmic metatheorems for a model checking problem P over infinite-state systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a large family of classes of infinite systems. Such results normally start with a powerful formalism F of infinite-state systems, over which P is undecidable, and assert decidability when is restricted by means of an extra “semantic condition ” C. We prove various algorithmic metatheorems for the problems of model checking LTL and its two common fragments LTL(Fs,Gs) and LTLdet over the expressive class of word/tree automatic transition systems, which are generated by synchronized finite-state transducers operating on finite words and trees. We present numerous applications, where we derive (in a unified manner) many known and previously unknown decidability and complexity results of model checking LTL and its fragments over specific classes of infinite-state systems including pushdown systems; prefix-recognizable systems; reversal-bounded counter systems with discrete clocks and a free counter; concurrent pushdown systems with a bounded number of context-switches; various subclasses of Petri nets; weakly extended PAprocesses; and weakly extended ground-tree rewrite systems. In all cases, we are able to derive optimal (or near optimal) complexity. Finally, we pinpoint the exact locations in the arithmetic and analytic hierarchies of the problem of checking a relevant semantic condition and the LTL model checking problems over all word/tree automatic systems.
When Model-Checking Freeze LTL over Counter Machines Becomes Decidable. Research report, LSV, ENS Cachan,
, 2010
"... Abstract. We study the decidability status of model-checking freeze LTL over various subclasses of counter machines for which the reachability problem is known to be decidable (reversal-bounded counter machines, vector additions systems with states, flat counter machines, one-counter machines). In ..."
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Abstract. We study the decidability status of model-checking freeze LTL over various subclasses of counter machines for which the reachability problem is known to be decidable (reversal-bounded counter machines, vector additions systems with states, flat counter machines, one-counter machines). In freeze LTL, a register can store a counter value and at some future position an equality test can be done between a register and a counter value. Herein, we complete an earlier work started on one-counter machines by considering other subclasses of counter machines, and especially the class of reversal-bounded counter machines. This gives us the opportuniy to provide a systematic classification that distinguishes determinism vs. nondeterminism and we consider subclasses of formulae by restricting the set of atomic formulae or/and the polarity of the occurrences of the freeze operators, leading to the flat fragment.
The Complexity of Reversal-Bounded Model-Checking ⋆
"... Abstract. We study model-checking problems on counter systems when guards are quantifier-free Presburger formulae, the specification languages are LTL-like dialects with arithmetical constraints and the runs are restricted to reversal-bounded ones. We introduce a generalization of reversal-boundedne ..."
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Abstract. We study model-checking problems on counter systems when guards are quantifier-free Presburger formulae, the specification languages are LTL-like dialects with arithmetical constraints and the runs are restricted to reversal-bounded ones. We introduce a generalization of reversal-boundedness and we show the NExpTime-completeness of the reversal-bounded model-checking problem as well as for related reversalbounded reachability problems. As a by-product, we show the effective Presburger definability for sets of configurations for which there is a reversal-bounded run verifying a given temporal formula. Our results generalize existing results about reversal-bounded counter automata and provides a uniform and more general framework. 1
The Existence of ω-Chains for Transitive Mixed Linear Relations and Its Applications
"... We show that it is decidable whether a transitive mixed linear relation has an omega-chain. Using this result... ..."
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We show that it is decidable whether a transitive mixed linear relation has an omega-chain. Using this result...
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
