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13
An Automata-Theoretic Approach to Constraint LTL
, 2003
"... We consider an extension of linear-time temporal logic (LTL) with constraints interpreted over a concrete domain. We use a new automata-theoretic technique to show pspace decidability of the logic for the constraint systems (Z, <, =) and (N, <, =). Along the way, we give an automata-theoretic ..."
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Cited by 32 (7 self)
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We consider an extension of linear-time temporal logic (LTL) with constraints interpreted over a concrete domain. We use a new automata-theoretic technique to show pspace decidability of the logic for the constraint systems (Z, <, =) and (N, <, =). Along the way, we give an automata-theoretic proof of a result of [BC02] when the constraint system D satisfies the completion property. Our decision procedures extend easily to handle extensions of the logic with past operators and constants, as well as an extension of the temporal language itself to monadic second order logic. Finally, we show that the logic...
Pushdown Timed Automata: a Binary Reachability Characterization and Safety Verification
- Theoretical Computer Science
, 2003
"... We consider pushdown timed automata (PTAs) that are timed automata (with dense clocks) augmented with a pushdown stack. A configuration of a PTA includes a state, dense clock values and a stack word. By using the pattern technique, we give a decidable characterization of the binary reachability ( ..."
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Cited by 21 (8 self)
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We consider pushdown timed automata (PTAs) that are timed automata (with dense clocks) augmented with a pushdown stack. A configuration of a PTA includes a state, dense clock values and a stack word. By using the pattern technique, we give a decidable characterization of the binary reachability (i.e., the set of all pairs of configurations such that one can reach the other) of a PTA. Since a timed automaton can be treated as a PTA without the pushdown stack, we can show that the binary reachability of a timed automaton is definable in the additive theory of reals and integers. The results can be used to verify a class of properties containing linear relations over both dense variables and unbounded discrete variables. The properties previously could not be verified using the classic region technique nor expressed by timed temporal logics for timed automata and CTL for pushdown systems. The results are also extended to other generalizations of timed automata.
Liveness verification of reversal-bounded multicounter machines with a free counter
- In FSTTCS’01, volume 2245 of LNCS
, 2001
"... Abstract. We investigate the Presburger liveness problems for nondeterministicreversal-bounded multicounter machines with a free counter (NCMFs). We show the following:-The 9-Presburger-i.o. problem and the 9-Presburger-eventual problem areboth decidable. So are their duals, the 8-Presburger-almost- ..."
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Cited by 17 (8 self)
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Abstract. We investigate the Presburger liveness problems for nondeterministicreversal-bounded multicounter machines with a free counter (NCMFs). We show the following:-The 9-Presburger-i.o. problem and the 9-Presburger-eventual problem areboth decidable. So are their duals, the 8-Presburger-almost-always problemand the 8-Presburger-always problem.- The 8-Presburger-i.o. problem and the 8-Presburger-eventual problem areboth undecidable. So are their duals, the 9-Presburger-almost-always prob-lem and the 9-Presburger-always problem. These results can be used to formulate a weak form of Presburger linear tem-poral logic and develop its model-checking theories for NCMFs. They can also be combined with [12] to study the same set of liveness problems on an extendedform of discrete timed automata containing, besides clocks, a number of reversalbounded counters and a free counter. 1 Introduction An infinite-state system can be obtained by augmenting a finite automaton with oneor more unbounded storage devices. The devices can be, for instance, counters (unary stacks), pushdown stacks, queues, and/or Turing tapes. However, an infinite-state sys-tem can easily achieve Turing-completeness, e.g., when two counters are attached to a finite automaton (resulting in a &quot;Minsky machine&quot;). For these systems, even simpleproblems such as membership are undecidable.
Binary Reachability Analysis of Pushdown Timed Automata with Dense Clocks
- In CAV’01, volume 2102 of LNCS
"... . We consider pushdown timed automata (PTAs) that are timed automata (with dense clocks) augmented with a pushdown stack. A configuration of a PTA includes a control state, dense clock values and a stack word. By using the pattern technique, we give a decidable characterization of the binary reachab ..."
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Cited by 15 (10 self)
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. We consider pushdown timed automata (PTAs) that are timed automata (with dense clocks) augmented with a pushdown stack. A configuration of a PTA includes a control state, dense clock values and a stack word. By using the pattern technique, we give a decidable characterization of the binary reachability (i.e., the set of all pairs of configurations such that one can reach the other) of a PTA. Since a timed automaton can be treated as a PTA without the pushdown stack, we can show that the binary reachability of a timed automaton is definable in the additive theory of reals and integers. The results can be used to verify a class of properties containing linear relations over both dense variables and unbounded discrete variables. The properties previously could not be verified using the classic region technique nor expressed by timed temporal logics for timed automata and CTL for pushdown systems. 1 Introduction A timed automaton [3] can be considered as a finite automaton augmented...
Presburger Liveness Verification of Discrete Timed Automata
, 2003
"... Using an automata-theoretic approach, we investigate the decidability of liveness properties (called Presburger liveness properties) for timed automata when Presburger formulas on configurations are allowed. While the general problem of checking a temporal logic such as TPTL augmented with Presburge ..."
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Cited by 8 (4 self)
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Using an automata-theoretic approach, we investigate the decidability of liveness properties (called Presburger liveness properties) for timed automata when Presburger formulas on configurations are allowed. While the general problem of checking a temporal logic such as TPTL augmented with Presburger clock constraints is undecidable, we show that there are various classes of Presburger liveness properties which are decidable for discrete timed automata. For instance, it is decidable, given a discrete timed automaton A and a Presburger property P , whether there exists an !-path of A where P holds infinitely often. We also show that other classes of Presburger liveness properties are indeed undecidable for discrete timed automata, e.g., whether P holds infinitely often for each !-path of A . These results might give insights into the corresponding problems for timed automata over dense domains, and help in the definition of a fragment of linear temporal logic, augmented with Presburger conditions on configurations, which is decidable for model checking timed automata.
Generalized discrete timed automata: decidable approximations for safety verification
- Theoretical Computer Science
"... Abstract. We consider generalized discrete timed automata with general linearrelations over clocks and parameterized constants as clock constraints and with parameterized durations. We look at three approximation techniques (i.e., the r-reset-bounded approximation, the B-bounded approximation, and t ..."
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Cited by 4 (4 self)
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Abstract. We consider generalized discrete timed automata with general linearrelations over clocks and parameterized constants as clock constraints and with parameterized durations. We look at three approximation techniques (i.e., the r-reset-bounded approximation, the B-bounded approximation, and the hB; ri-crossing-bounded approximation), and derive automata-theoretic characterizations of the binary reachability under these approximations. The characteriza-tions allow us to show that the safety analysis problem is decidable for generalized discrete timed automata with unit durations and for deterministic generalizeddiscrete timed automata with parameterized durations. An example specification written in ASTRAL is used to run a number of experiments using one of theapproximation techniques. 1 Introduction As a standard model for analyzing real-time systems, timed automata [3] have receivedenormous attention during the past decade. A timed automaton can be considered as a finite automaton augmented with a finite number of clocks. The clocks can be reset orprogress at the same rate, and can be tested against clock constraints in the form of clock regions (i.e., comparisons of a clock or the difference of two clocks against an integerconstant, e.g.,
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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Cited by 3 (2 self)
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We show that it is decidable whether a transitive mixed linear relation has an omega-chain. Using this result...
Dense counter machines and verification problems, in
- CAV, LNCS
"... Abstract. We generalize the traditional definition of a multicounter machine (where the counters, which can only assume nonnegative integer values, can be incremented/decremented by 1 and tested for zero) by allowing the machine the additional ability to increment/decrement the counters by a nondete ..."
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Cited by 3 (0 self)
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Abstract. We generalize the traditional definition of a multicounter machine (where the counters, which can only assume nonnegative integer values, can be incremented/decremented by 1 and tested for zero) by allowing the machine the additional ability to increment/decrement the counters by a nondeterministically chosen fractional amount between 0 and 1 (the may be different at each step). We show that, under some restrictions on counter behavior, the binary reachability set of such a machine is definable in the additive theory of the reals and integers. There are applications of this result in verification, and we give one example in the paper. We also extend the notion of “semilinear language” to “dense semilinear language ” and show its connection to a restricted class of dense multicounter automata.
Decidable Approximations on Generalized and Parameterized Discrete Timed Automata
- COCOON'01, LNCS 2108
"... . We consider generalized discrete timed automata with general linear relations over clocks and parameterized constants as clock constraints and with parameterized durations. We look at three approximation techniques (i.e., the r-reset-bounded approximation, the B-bounded approximation, and the hB ..."
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Cited by 2 (2 self)
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. We consider generalized discrete timed automata with general linear relations over clocks and parameterized constants as clock constraints and with parameterized durations. We look at three approximation techniques (i.e., the r-reset-bounded approximation, the B-bounded approximation, and the hB; ri-crossing-bounded approximation), and derive automata-theoretic characterizations of the binary reachability under these approximations. The characterizations allow us to show that the safety analysis problem is decidable for generalized discrete timed automata with unit durations and for deterministic generalized discrete timed automata with parameterized durations. An example specification written in ASTRAL is used to run a number of experiments using one of the approximation techniques. 1
New complexity results for some linear counting problems using minimal solutions to linear diophantine equations (Extended Abstract)
, 2003
"... The linear reachability problem 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 results on minimal solutions (in nonnegative integers) for linear Diophantine systems, we obta ..."
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The linear reachability problem 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 results on minimal solutions (in nonnegative integers) for linear Diophantine systems, we obtain new complexity results for the problem, as well as for other linear counting problems of finite state transition systems and timed automata. In contrast to previously known results, the complexity bounds obtained in this paper are polynomial in the size of the transition system in consideration, when the linear constraint is fixed.
