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21
ContextBounded Analysis of Concurrent Queue Systems ⋆
"... Abstract. We show that the bounded contextswitching reachability problem for concurrent finite systems communicating using unbounded FIFO queues is decidable, where in each context a process reads from only one queue (but is allowed to write onto all other queues). Our result also holds when indivi ..."
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Cited by 19 (3 self)
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Abstract. We show that the bounded contextswitching reachability problem for concurrent finite systems communicating using unbounded FIFO queues is decidable, where in each context a process reads from only one queue (but is allowed to write onto all other queues). Our result also holds when individual processes are finitestate recursive programs provided a process dequeues messages only when its local stack is empty. We then proceed to classify architectures that admit a decidable (unbounded context switching) reachability problem, using the decidability of bounded context switching. We show that the precise class of decidable architectures for recursive programs are the forest architectures, while the decidable architectures for nonrecursive programs are those that do not have an undirected cycle. 1
Emptiness of multipushdown automata is 2ETIMEcomplete
"... Abstract. We consider multipushdown automata, a multistack extension of pushdown automata that comes with a constraint on stack operations: a pop can only be performed on the first nonempty stack (which implies that we assume a linear ordering on the collection of stacks). We show that the emptin ..."
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Cited by 9 (3 self)
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Abstract. We consider multipushdown automata, a multistack extension of pushdown automata that comes with a constraint on stack operations: a pop can only be performed on the first nonempty stack (which implies that we assume a linear ordering on the collection of stacks). We show that the emptiness problem for multipushdown automata is 2ETIMEcomplete wrt. the number of stacks. Containment in 2ETIME is shown by translating an automaton into a grammar for which we can check if the generated language is empty. The lower bound is established by simulating the behavior of an alternating Turing machine working in exponential space. We also compare multipushdown automata with the model of boundedphase multistack (visibly) pushdown automata. 1
Reachability analysis of communicating pushdown systems
 In FOSSACS
, 2010
"... Abstract. 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 w ..."
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Cited by 9 (1 self)
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Abstract. 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.
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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Cited by 8 (1 self)
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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]:
MSO decidability of multipushdown systems via splitwidth. Research Report LSV1211, Laboratoire Spécification et Vérification, ENS
, 2012
"... Abstract. 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. An ..."
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Cited by 5 (0 self)
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Abstract. 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 a 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. 1
Scopebounded Multistack Pushdown Systems: FixedPoint, Sequentialization, and TreeWidth
"... Abstract. Wepresentanovelfixedpointalgorithmtosolvereachability 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 impl ..."
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Cited by 5 (1 self)
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Abstract. Wepresentanovelfixedpointalgorithmtosolvereachability 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. 1
Analyzing Asynchronous Programs with Preemption
"... ABSTRACT. Multiset pushdown systems have been introduced by Sen and Viswanathan as an adequate model for asynchronous programs where some procedure calls can be stored as tasks to be processed later. The model is a pushdown system supplied with a multiset of pending tasks. Tasks may be added to the ..."
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Cited by 4 (2 self)
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ABSTRACT. Multiset pushdown systems have been introduced by Sen and Viswanathan as an adequate model for asynchronous programs where some procedure calls can be stored as tasks to be processed later. The model is a pushdown system supplied with a multiset of pending tasks. Tasks may be added to the multiset at each transition, whereas a task is taken from the multiset only when the stack is empty. In this paper, we consider an extension of these models where tasks may be of different priority level, and can be preempted at any point of their execution by tasks of higher priority. We investigate the control point reachability problem for these models. Our main result is that this problem is decidable by reduction to the reachability problem for a decidable class of Petri nets with inhibitor arcs. We also identify two subclasses of these models for which the control point reachability problem is reducible respectively to the reachability problem and to the coverability problem for Petri nets (without inhibitor arcs). 1
Realizability of Concurrent Recursive Programs
, 2008
"... We define and study an automata model of concurrent recursive programs. An automaton consists of a finite number of pushdown systems running in parallel and communicating via shared actions. Actually, we combine multistack visibly pushdown automata and Zielonka’s asynchronous automata towards a mod ..."
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Cited by 3 (1 self)
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We define and study an automata model of concurrent recursive programs. An automaton consists of a finite number of pushdown systems running in parallel and communicating via shared actions. Actually, we combine multistack visibly pushdown automata and Zielonka’s asynchronous automata towards a model with an undecidable emptiness problem. However, a reasonable restriction allows us to lift Zielonka’s Theorem to this recursive setting and permits a logical characterization in terms of a suitable monadic secondorder logic. Building on results from Mazurkiewicz trace theory and recent work by La Torre, Madhusudan, and Parlato, we thus develop a framework for the specification, synthesis, and verification of concurrent recursive processes.
An Infinite Automaton Characterization of Double Exponential Time
"... Infinitestate automata are a new invention: they are automata that have an infinite number of states represented by words, transitions defined using rewriting, and with sets of initial and final states. Infinitestate automata have gained recent interest due to a remarkable result by Morvan and Sti ..."
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Cited by 3 (2 self)
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Infinitestate automata are a new invention: they are automata that have an infinite number of states represented by words, transitions defined using rewriting, and with sets of initial and final states. Infinitestate automata have gained recent interest due to a remarkable result by Morvan and Stirling, which shows that automata with transitions defined using rational rewriting precisely capture contextsensitive (NLINSPACE) languages. In this paper, we show that infinite automata defined using a form of multistack rewriting precisely defines double exponential time (more precisely, 2ETIME, the class of problems solvable in 2 2O(n) time). The salient aspect of this characterization is that the automata have no ostensible limits on time nor space, and neither direction of containment with respect to 2ETIME is obvious. In this sense, the result captures the complexity class qualitatively, by restricting the power of rewriting.
Model Checking Languages of Data Words ⋆
"... Abstract. We consider the modelchecking problem for data multipushdown automata (DMPA). DMPA generate data words, i.e, strings enriched with values from an infinite domain. The latter can be used to represent an unbounded number of process identifiers so that DMPA are suitable to model concurrent p ..."
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Cited by 3 (1 self)
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Abstract. We consider the modelchecking problem for data multipushdown automata (DMPA). DMPA generate data words, i.e, strings enriched with values from an infinite domain. The latter can be used to represent an unbounded number of process identifiers so that DMPA are suitable to model concurrent programs with dynamic process creation. To specify properties of data words, we use monadic secondorder (MSO) logic, which comes with a predicate to test two word positions for data equality. While satisfiability for MSO logic is undecidable (even for weaker fragments such as firstorder logic), our main result states that one can decide if all words generated by a DMPA satisfy a given formula from the full MSO logic. 1