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Model checking freeze LTL over onecounter automata
, 2008
"... We study complexity issues related to the modelchecking problem for LTL with registers (a.k.a. freeze LTL) over onecounter automata. We consider several classes of onecounter 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 modelchecking problem for LTL with registers (a.k.a. freeze LTL) over onecounter automata. We consider several classes of onecounter 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 nontrivial abstraction on counter values, we show that model checking LTL with registers over deterministic onecounter automata is PSPACEcomplete with infinite accepting runs. By constrast, we prove that model checking LTL with registers over nondeterministic onecounter automata is Σ 1 1complete [resp. Σ 0 1complete] 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 onecounter 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 modelchecking LTL with registers over other classes of operational models, such as reversalbounded counter machines and deterministic pushdown systems.
Composability of infinitestate 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, alookahead 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 adelegator for any. We look at the decidability of composability and existence ofdelegators for various classes of machines. Our results have applications to automated composition of eservices. E
Reversalbounded counter machines revisited
, 2008
"... We extend the class of reversalbounded counter machines by authorizing a finite number of alternations between increasing and decreasing mode over a given bound. We prove that extended reversalbounded counter machines also have effective semilinear 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 reversalbounded counter machines by authorizing a finite number of alternations between increasing and decreasing mode over a given bound. We prove that extended reversalbounded counter machines also have effective semilinear reachability sets. We also prove that the property of being reversalbounded 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 reversalboundedness 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, reversalboundedness 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 polynomialspace 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 infinitestate 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 infinitestate 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 infinitestate 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 finitestate 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 infinitestate systems including pushdown systems; prefixrecognizable systems; reversalbounded counter systems with discrete clocks and a free counter; concurrent pushdown systems with a bounded number of contextswitches; various subclasses of Petri nets; weakly extended PAprocesses; and weakly extended groundtree 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 ModelChecking Freeze LTL over Counter Machines Becomes Decidable. Research report, LSV, ENS Cachan,
, 2010
"... Abstract. We study the decidability status of modelchecking freeze LTL over various subclasses of counter machines for which the reachability problem is known to be decidable (reversalbounded counter machines, vector additions systems with states, flat counter machines, onecounter machines). In ..."
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Abstract. We study the decidability status of modelchecking freeze LTL over various subclasses of counter machines for which the reachability problem is known to be decidable (reversalbounded counter machines, vector additions systems with states, flat counter machines, onecounter 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 onecounter machines by considering other subclasses of counter machines, and especially the class of reversalbounded 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 ReversalBounded ModelChecking ⋆
"... Abstract. We study modelchecking problems on counter systems when guards are quantifierfree Presburger formulae, the specification languages are LTLlike dialects with arithmetical constraints and the runs are restricted to reversalbounded ones. We introduce a generalization of reversalboundedne ..."
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Abstract. We study modelchecking problems on counter systems when guards are quantifierfree Presburger formulae, the specification languages are LTLlike dialects with arithmetical constraints and the runs are restricted to reversalbounded ones. We introduce a generalization of reversalboundedness and we show the NExpTimecompleteness of the reversalbounded modelchecking problem as well as for related reversalbounded reachability problems. As a byproduct, we show the effective Presburger definability for sets of configurations for which there is a reversalbounded run verifying a given temporal formula. Our results generalize existing results about reversalbounded counter automata and provides a uniform and more general framework. 1
The Existence of ωChains for Transitive Mixed Linear Relations and Its Applications
"... We show that it is decidable whether a transitive mixed linear relation has an omegachain. Using this result... ..."
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We show that it is decidable whether a transitive mixed linear relation has an omegachain. Using this result...
Realcounter automata and their decision problems
 in: FSTTCS, LNCS 3328
"... Abstract. We introduce realcounter automata, which are twoway finite automata augmented with counters that take real values. In contrast to traditional word automata that accept sequences of symbols, realcounter automata accept real words that are bounded and closed real intervals delimited by a ..."
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Abstract. We introduce realcounter automata, which are twoway finite automata augmented with counters that take real values. In contrast to traditional word automata that accept sequences of symbols, realcounter 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 oneway/twoway realcounter automata as well as those automata further augmented with other unbounded storage devices such as integercounters 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 worstcase time complexity result for the linear reachability problem for timed automata. Key words: Modelchecking, timed automata, reachability, linear Diophantine equation systems, minimal solutions 1