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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.
A Note on the Complexity of ModelChecking Bounded MultiPushdown Systems
, 2012
"... In this note, we provide complexity characterizations of model checking multipushdown systems. Multipushdown systems model recursive concurrent programs in which any sequential process has a finite control. We consider three standard notions for boundedness: context boundedness, phase boundedness ..."
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In this note, we provide complexity characterizations of model checking multipushdown systems. Multipushdown systems model recursive concurrent programs in which any sequential process has a finite control. We consider three standard notions for boundedness: context boundedness, phase boundedness and stack ordering. The logical formalism is a lineartime temporal logic extending wellknown logic CaRet but dedicated to multipushdown systems in which abstract operators (related to calls and returns) such as those for nexttime and until are parameterized by stacks. We show that the problem is EXPTIMEcomplete for contextbounded runs and unary encoding of the number of context switches; we also prove that the problem is 2EXPTIMEcomplete for phasebounded runs and unary encoding of the number of phase switches. In both cases, the value k is given as an input (whence it is not a constant of the modelchecking problem), which makes a substantial difference in the complexity. In certain cases, our results improve previous complexity results.
ModelChecking Bounded MultiPushdown Systems
"... We provide complexity characterizations of model checking multipushdown systems. We consider three standard notions for boundedness: context boundedness, phase boundedness and stack ordering. The logical formalism is a lineartime temporal logic extending wellknown operators are parameterized b ..."
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We provide complexity characterizations of model checking multipushdown systems. We consider three standard notions for boundedness: context boundedness, phase boundedness and stack ordering. The logical formalism is a lineartime temporal logic extending wellknown operators are parameterized by stacks. We show that the problem is ExpTimecomplete for contextbounded runs and unary encoding of the number of context switches; we also prove that the problem is 2ExpTimecomplete for phasebounded runs and unary encoding of the number of phase switches. In both cases, the value k is given as an input, which makes a substantial difference in the complexity.