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Liveness verification of reversalbounded multicounter machines with a free counter
 In FSTTCS’01, volume 2245 of LNCS
, 2001
"... Abstract. We investigate the Presburger liveness problems for nondeterministicreversalbounded multicounter machines with a free counter (NCMFs). We show the following:The 9Presburgeri.o. problem and the 9Presburgereventual problem areboth decidable. So are their duals, the 8Presburgeralmost ..."
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Abstract. We investigate the Presburger liveness problems for nondeterministicreversalbounded multicounter machines with a free counter (NCMFs). We show the following:The 9Presburgeri.o. problem and the 9Presburgereventual problem areboth decidable. So are their duals, the 8Presburgeralmostalways problemand the 8Presburgeralways problem. The 8Presburgeri.o. problem and the 8Presburgereventual problem areboth undecidable. So are their duals, the 9Presburgeralmostalways problem and the 9Presburgeralways problem. These results can be used to formulate a weak form of Presburger linear temporal logic and develop its modelchecking 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 infinitestate 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 infinitestate system can easily achieve Turingcompleteness, 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.
Past Pushdown Timed Automata and Safety Verification
 Theoretical Computer Science
"... We consider past pushdown timed automata that are discrete pushdown timed automata with past formulas as enabling conditions. Using past formulas allows a past pushdown timed automaton to access the past values of the finite state variables in the automaton. We prove that the reachability (i.e., the ..."
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Cited by 6 (0 self)
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We consider past pushdown timed automata that are discrete pushdown timed automata with past formulas as enabling conditions. Using past formulas allows a past pushdown timed automaton to access the past values of the finite state variables in the automaton. We prove that the reachability (i.e., the set of reachable configurations from an initial configuration) of a past pushdown timed automaton can be accepted by a nondeterministic reversalbounded counter machine augmented with a pushdown stack (i.e., a reversalbounded NPCM). By using the known fact that the emptiness problem for reversalbounded NPCMs is decidable, we show that modelchecking past pushdown timed automata against Presburger safety properties on discrete clocks and stack word counts is decidable. We also investigate the reachability problem for a class of transition systems under some fairness constraints in the form of generalized past formulas. Finally, we present an example ASTRAL specification to demonstrate the usefulness of the results.
Software Tools for Technology Transfer manuscript No. (will be inserted by the editor) Parallel Search for LTL Violations
"... Abstract. Recent advances in parallel model checking for liveness properties achieve significant capacity increases over sequential model checkers. However, the capacity of parallel model checkers is in turn limited by available aggregate memory and network bandwidth. We propose a new parallel algor ..."
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Abstract. Recent advances in parallel model checking for liveness properties achieve significant capacity increases over sequential model checkers. However, the capacity of parallel model checkers is in turn limited by available aggregate memory and network bandwidth. We propose a new parallel algorithm that sacrifices complete coverage for increased capacity to find errors. The algorithm, called BEE (for beebased error exploration) uses coordinated depthbounded random walks to reduce memory and bandwidth demands. A unique advantage of BEE is that it is wellsuited for use on clusters of nondedicated workstations.
Approximation Techniques for Using the ASTRAL Symbolic Model Checker as a Specification Debugger
"... ASTRAL is a highlevel formal speci cation language for realtime systems. This paper presents a symbolic model checker that translates an ASTRAL process instance to a labeled transition system with each transition representable by a Presburger formula. The labeled transition system is unfolded into ..."
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ASTRAL is a highlevel formal speci cation language for realtime systems. This paper presents a symbolic model checker that translates an ASTRAL process instance to a labeled transition system with each transition representable by a Presburger formula. The labeled transition system is unfolded into the execution tree of an ASTRAL process and the Omega library is used to carry out the image computations. Different levels of approximation of the environment behaviors of the instance are considered, as well as symbolic search strategies including depthfirst search, breadthfirst search, and depthbreadth search. Three approximation techniques to speed up the model checking process for use in debugging a speci cation are also presented. They are random walk, partial image and dynamic environment generation. Ten mutation tests on a railroad crossing benchmark are used to compare the performance of the techniques applied separately and in combination. The test results are presented and analyzed.