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The Tree Width of Auxiliary Storage
"... We propose a generalization of results on the decidability of emptiness for several restricted classes of sequential and distributed automata with auxiliary storage (stacks, queues) that have recently been proved. Our generalization relies on reducing emptiness of these automata to finitestate grap ..."
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We propose a generalization of results on the decidability of emptiness for several restricted classes of sequential and distributed automata with auxiliary storage (stacks, queues) that have recently been proved. Our generalization relies on reducing emptiness of these automata to finitestate graph automata (without storage) restricted to monadic secondorder (MSO) definable graphs of bounded treewidth, where the graph structure encodes the mechanism provided by the auxiliary storage. Our results outline a uniform mechanism to derive emptiness algorithms for automata, explaining and simplifying several existing results, as well as proving new decidability results. Categories and Subject Descriptors F.1.1 [Theory of Computation]:
Reachability analysis of communicating pushdown systems
, 2009
"... The reachability analysis of recursive programs that communicate asynchronously over reliable Fifo channels calls for restrictions to ensure decidability. We extend here a model proposed by La Torre, Madhusudan and Parlato [LMP08], based on communicating pushdown systems that can dequeue with empt ..."
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Cited by 21 (3 self)
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The reachability analysis of recursive programs that communicate asynchronously over reliable Fifo channels calls for restrictions to ensure decidability. We extend here a model proposed by La Torre, Madhusudan and Parlato [LMP08], based on communicating pushdown systems that can dequeue with empty stack only. Our extension adds the dual modality, which allows to dequeue with nonempty stack, and thus models interrupts for working threads. We study (possibly cyclic) network architectures under a semantic assumption on communication that ensures the decidability of reachability for finite state systems. Subsequently, we determine precisely how pushdowns can be added to this setting while preserving the decidability; in the positive case we obtain exponential time as the exact complexity bound of reachability. A second result is a generalization of the doubly exponential time algorithm of [LMP08] for bounded context analysis to our symmetric queueing policy. We provide here a direct and simpler algorithm.
MSO decidability of MultiPushdown Systems via SplitWidth
, 2012
"... Multithreaded programs with recursion are naturally modeled as multipushdown systems. The behaviors are represented as multiply nested words (MNWs), which are words enriched with additional binary relations for each stack matching a push operation with the corresponding pop operation. Any MNW ca ..."
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Cited by 15 (4 self)
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Multithreaded programs with recursion are naturally modeled as multipushdown systems. The behaviors are represented as multiply nested words (MNWs), which are words enriched with additional binary relations for each stack matching a push operation with the corresponding pop operation. Any MNW can be decomposed by two basic and natural operations: shuffle of two sequences of factors and merge of consecutive factors of a sequence. We say that the splitwidth of an MNW is k if it admits a decomposition where the number of factors in each sequence is at most k. The MSO theory of MNWs with splitwidth k is decidable. We introduce two very general classes of MNWs that strictly generalize known decidable classes and prove their MSO decidability via their splitwidth and obtain comparable or better bounds of treewidth of known classes.
Temporal logics for concurrent recursive programs: Satisfiability and model checking
 In MFCS’11, volume 6907 of LNCS
, 2011
"... Abstract. We develop a general framework for the design of temporal logics for concurrent recursive programs. A program execution is modeled as a partial order with multiple nesting relations. To specify properties of executions, we consider any temporal logic whose modalities aredefinable in monadi ..."
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Cited by 9 (3 self)
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Abstract. We develop a general framework for the design of temporal logics for concurrent recursive programs. A program execution is modeled as a partial order with multiple nesting relations. To specify properties of executions, we consider any temporal logic whose modalities aredefinable in monadic secondorder logic and that, in addition, allows PDLlike path expressions. This captures, in a unifying framework, a wide range of logics defined for ranked and unranked trees, nested words, and Mazurkiewicz traces that have been studied separately. We show that satisfiability and model checking are decidable in EXPTIME and 2EXPTIME, depending on the precise path modalities. 1
Bounded phase analysis of messagepassing programs
, 2012
"... We describe a novel technique for bounded analysis of asynchronous messagepassing programs with ordered message queues. Our bounding parameter does not limit the number of pending messages, nor the number of “contextsswitches” between processes. Instead, we limit the number of process communicat ..."
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Cited by 9 (1 self)
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We describe a novel technique for bounded analysis of asynchronous messagepassing programs with ordered message queues. Our bounding parameter does not limit the number of pending messages, nor the number of “contextsswitches” between processes. Instead, we limit the number of process communication cycles, in which an unbounded number of messages are sent to an unbounded number of processes across an unbounded number of contexts. We show that remarkably, despite the potential for such vast exploration, our bounding scheme gives rise to a simple and efficient program analysis by reduction to sequential programs. As our reduction avoids explicitly representing message queues, our analysis scales irrespectively of queue content and variation.
Lineartime modelchecking for multithreaded programs under scopebounding
 In Supratik Chakraborty and Madhavan Mukund, editors, ATVA, volume 7561 of Lecture Notes in Computer Science
, 2012
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Saturation of Concurrent Collapsible Pushdown Systems
"... Multistack pushdown systems are a wellstudied model of concurrent computation using threads with firstorder procedure calls. While, in general, reachability is undecidable, there are numerous restrictions on stack behaviour that lead to decidability. To model higherorder procedures calls, a gene ..."
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Cited by 5 (2 self)
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Multistack pushdown systems are a wellstudied model of concurrent computation using threads with firstorder procedure calls. While, in general, reachability is undecidable, there are numerous restrictions on stack behaviour that lead to decidability. To model higherorder procedures calls, a generalisation of pushdown stacks called collapsible pushdown stacks are required. Reachability problems for multistack collapsible pushdown systems have been little studied. Here, we study ordered, phasebounded and scopebounded multistack collapsible pushdown systems using saturation techniques, showing decidability of control state reachability and giving a regular representation of all configurations that can reach a given control state.
From multi to single stack automata
 In Proc. of CONCUR 2010, volume 6269 of LNCS
, 2010
"... Abstract. Verification of concurrent programs modelled as multistack machines is an active research area. Recently decidability/complexity results have been established for powerful models such as boundedphase visibly pushdown automata (BVMPA) [16] and ordered multipushdown automata (OMPA) [1]. ..."
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Cited by 5 (2 self)
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Abstract. Verification of concurrent programs modelled as multistack machines is an active research area. Recently decidability/complexity results have been established for powerful models such as boundedphase visibly pushdown automata (BVMPA) [16] and ordered multipushdown automata (OMPA) [1]. However, the proofs of these results are quite complex and are based on different techniques and concepts for each of the considered models. We investigate in this paper the issue of reducing the verification problem of multistack machines to the one for singlestack machines. We believe that this is a general paradigm for understanding the expressive power and for establishing decidability results for various classes of concurrent program models. For instance, elegant (and paractically efficient) algorithms for boundedcontext switch analysis of multipushdown systems have been recently defined based on reductions to the reachability problem of (singlestack) pushdown systems [10, 18]. We extend this view to both OMPA and BVMPA by showing that each of their emptiness problems can be reduced to the one for a class of singlestack machines. For these reductions, we introduce effective generalized pushdown automata (EGPA) where operations on stacks are (1) pop the top symbol of the stack, and (2) push a word in some (effectively) given set of words L over the stack alphabet, assuming that L is in some class of languages for which checking whether L intersects a given regular language is decidable. We show that the automatabased saturation procedure for computing the set of predecessors in standard pushdown automata can be easily extended to prove that for EGPA too the set of all predecessors of a regular set of configurations is an effectively constructible regular set. Our reductions from OMPA and BVMPA to EGPA, together with the reachability analysis procedure for EGPA, allow to provide conceptually simple algorithms for checking the emptiness problem for each of these models, and to significantly simplify the proofs for their 2ETIME upper bounds (matching their lowerbounds). 1
Modelchecking of ordered multipushdown automata
 Log. Methods Comput. Sci
"... Vol. 8(3:20)2012, pp. 1–31 ..."
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On the expressive power of 2stack visibly pushdown automata
 LMCS
, 2008
"... Abstract. Visibly pushdown automata are inputdriven pushdown automata that recognize some nonregular contextfree languages while preserving the nice closure and decidability properties of finite automata. Visibly pushdown automata with multiple stacks have been considered recently by La Torre, Ma ..."
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Abstract. Visibly pushdown automata are inputdriven pushdown automata that recognize some nonregular contextfree languages while preserving the nice closure and decidability properties of finite automata. Visibly pushdown automata with multiple stacks have been considered recently by La Torre, Madhusudan, and Parlato, who exploit the concept of visibility further to obtain a rich automata class that can even express properties beyond the class of contextfree languages. At the same time, their automata are closed under boolean operations, have a decidable emptiness and inclusion problem, and enjoy a logical characterization in terms of a monadic secondorder logic over words with an additional nesting structure. These results require a restricted version of visibly pushdown automata with multiple stacks whose behavior can be split up into a fixed number of phases. In this paper, we consider 2stack visibly pushdown automata (i.e., visibly pushdown automata with two stacks) in their unrestricted form. We show that they are expressively equivalent to the existential fragment of monadic secondorder logic. Furthermore, it turns out that monadic secondorder quantifier alternation forms an infinite hierarchy wrt. words with multiple nestings. Combining these results, we conclude that 2stack visibly pushdown automata are not closed under complementation. Finally, we discuss the expressive power of Büchi 2stack visibly pushdown automata running on infinite (nested) words. Extending the logic by an infinity quantifier, we can likewise establish equivalence to existential monadic secondorder logic. 1.