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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
Pairwise Reachability Analysis for Higher Order Concurrent Programs by HigherOrder Model Checking
"... Abstract. We propose a sound, complete, and automatic method for pairwise reachability analysis of higherorder concurrent programs with recursion, nested locks, joins, and dynamic thread creation. The method is based on a reduction to higherorder model checking (i.e., model checking of trees gene ..."
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Abstract. We propose a sound, complete, and automatic method for pairwise reachability analysis of higherorder concurrent programs with recursion, nested locks, joins, and dynamic thread creation. The method is based on a reduction to higherorder model checking (i.e., model checking of trees generated by higherorder recursion schemes). It can be considered an extension of Gawlitz et al.’s work on the joinlocksensitive reachability analysis for dynamic pushdown networks (DPN) to higherorder programs. To our knowledge, this is the first application of higherorder model checking to sound and complete verification of (reasonably expressive models of) concurrent programs. 1
Unboundedness and Downward Closures of HigherOrder Pushdown Automata
"... We show the diagonal problem for higherorder pushdown automata (HOPDA), and hence the simultaneous unboundedness problem, is decidable. From recent work by Zetzsche this means that we can construct the downward closure of the set of words accepted by a given HOPDA. This also means we can construct ..."
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We show the diagonal problem for higherorder pushdown automata (HOPDA), and hence the simultaneous unboundedness problem, is decidable. From recent work by Zetzsche this means that we can construct the downward closure of the set of words accepted by a given HOPDA. This also means we can construct the downward closure of the Parikh image of a HOPDA. Both of these consequences play an important rôle in verifying concurrent higherorder programs expressed as HOPDA or safe higherorder recursion schemes.
HigherOrder ModelChecking and Underapproximate Models of Concurrent Recursive Programs
"... Pushdown automata (PDA) are a good model of recursive programs which also have good algorithmic properties. For example “reachability ” for PDA is decidable, allowing one to automatically check whether a program modelled by the PDA is “safe”—i.e. that it cannot “reach an error state”. But what happe ..."
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Pushdown automata (PDA) are a good model of recursive programs which also have good algorithmic properties. For example “reachability ” for PDA is decidable, allowing one to automatically check whether a program modelled by the PDA is “safe”—i.e. that it cannot “reach an error state”. But what happens if one wants to model a recursive program featuring more than one thread of execution? A nave idea would be to generalise pushdown automata by allowing them multiple stacks—one for each thread. Unfortunately, as is well known, PDAs with more than one stack are as powerful as Turing machines; this precludes the possibility of them having any interesting decidable properties. One possible approach to this problem is to impose constraints on the ways in which multistack PDA can use their stacks. On the plus side these constraints should produce a model for which reachability is decidable. On the down side, the constrained model will in general only be able to “underapproximate ” the behaviour of concurrent recursive programs—the program may