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Scopebounded Multistack Pushdown Systems: FixedPoint, Sequentialization, and TreeWidth
, 2012
"... We present a novel fixedpoint algorithm to solve reachability of multistack pushdown systems restricted to runs of boundedscope. The followed approach is compositional, in the sense that the runs of the system are summarized by boundedsize interfaces. Moreover, it is suitable for a direct implem ..."
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We present a novel fixedpoint algorithm to solve reachability of multistack pushdown systems restricted to runs of boundedscope. The followed approach is compositional, in the sense that the runs of the system are summarized by boundedsize interfaces. Moreover, it is suitable for a direct implementation and can be exploited to prove two new results. We give a sequentialization for this class of systems, i.e., for each such multistack pushdown system we construct an equivalent singlestack pushdown system that faithfully simulates the behaviour of each thread. We prove that the behaviour graphs (multiply nested words) for these systems have bounded threewidth, and thus a number of decidability results can be derived from Courcelle’s theorem.
The complexity of modelchecking multistack systems
, 2012
"... Abstract—We consider the lineartime model checking problem for boolean concurrent programs with recursive procedure calls. While sequential recursive programs are usually modeled as pushdown automata, concurrent recursive programs involve several processes and can be naturally abstracted as pushdo ..."
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Cited by 4 (0 self)
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Abstract—We consider the lineartime model checking problem for boolean concurrent programs with recursive procedure calls. While sequential recursive programs are usually modeled as pushdown automata, concurrent recursive programs involve several processes and can be naturally abstracted as pushdown automata with multiple stacks. Their behavior can be understood as words with multiple nesting relations, each relation connecting a procedure call with its corresponding return. To reason about multiply nested words, we consider the class of all temporal logics as defined in the book by Gabbay, Hodkinson, and Reynolds (1994). The unifying feature of these temporal logics is that their modalities are defined in monadic secondorder (MSO) logic. In particular, this captures numerous temporal logics over concurrent and/or recursive programs that have been defined so far. Since the general model checking problem is undecidable, we restrict attention to phase bounded executions as proposed by La Torre, Madhusudan, and Parlato (LICS 2007). While the MSO model checking problem in this case is nonelementary, our main result states that the model checking (and satisfiability) problem for all these temporal logics is decidable in elementary time. More precisely, it is solvable in (n + 2)EXPTIME where n is the maximal level of the MSO modalities in the monadic quantifier alternation hierarchy. We complement this result and provide, for each level n, a temporal logic whose model checking problem is nEXPSPACEhard. I.
ScopeBounded Pushdown Languages
"... Abstract. We study the formal language theory of multistack pushdown automata (Mpa) restricted to computations where a symbol can be popped from a stack S only if it was pushed within a bounded number of contexts of S (scoped Mpa). We contribute to show that scoped Mpa are indeed a robust model of ..."
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Abstract. We study the formal language theory of multistack pushdown automata (Mpa) restricted to computations where a symbol can be popped from a stack S only if it was pushed within a bounded number of contexts of S (scoped Mpa). We contribute to show that scoped Mpa are indeed a robust model of computation, by focusing on the corresponding theory of visibly Mpa (Mvpa). We prove the equivalence of the deterministic and nondeterministic versions and show that scopebounded computations of an nstack Mvpa can be simulated, rearranging the input word, by using only one stack. These results have several interesting consequences, such as, the closure under complement, the decidability of universality, inclusion and equality, and a Parikh theorem. We also give a logical characterization and compare the expressiveness of the scopebounded restriction with Mvpa classes from the literature. 1
A Unifying Approach for Multistack Pushdown Automata (Track B)
, 2014
"... We give a general approach to show the closure under complement and decide the emptiness for many classes of multistack visibly pushdown automata (Mvpa). A central notion in our approach is the visibly pathtree, i.e., a stack tree with the encoding of a path that denotes a linear ordering of the no ..."
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We give a general approach to show the closure under complement and decide the emptiness for many classes of multistack visibly pushdown automata (Mvpa). A central notion in our approach is the visibly pathtree, i.e., a stack tree with the encoding of a path that denotes a linear ordering of the nodes. We show that the set of all such trees with a bounded size labeling is regular, and pathtrees allow us to design simple conversions between tree automata and Mvpa’s. As corollaries of our results we get the closure under complement of ordered Mvpa that was an open problem, and a better upper bound on the algorithm to check the emptiness of boundedphase Mvpa’s, that also shows that this problem is fixed parameter tractable in the number of phases.