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15
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 12 (2 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
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
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.
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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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.
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.
Verifying Communicating Multipushdown Systems
"... Abstract. Communicating multipushdown systems model networks of multithreaded recursive programs communicating via reliable FIFO channels. Hence their verification problems are undecidable in general. The behaviours of these systems can be represented as directed graphs, which subsume both Message ..."
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Abstract. Communicating multipushdown systems model networks of multithreaded recursive programs communicating via reliable FIFO channels. Hence their verification problems are undecidable in general. The behaviours of these systems can be represented as directed graphs, which subsume both Message Sequence Charts and nested words. We extend the notion of splitwidth [8] to these graphs, defining a simple algebra to compose/decompose these behaviours using two natural operations: shuffle and merge. We obtain simple, uniform and optimal decision procedures for various verification problems parametrized by splitwidth, ranging from reachability to modelchecking against MSO, PDL and Temporal Logics. 1
Reasoning about distributed systems: WYSIWYG (invited talk
 In Proceedings of the 34th Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS’14), Leibniz International Proceedings in Informatics. LeibnizZentrum für Informatik
, 2014
"... There are two schools of thought on reasoning about distributed systems: one following interleaving based semantics, and one following partialorder/graph based semantics. This paper compares these two approaches and argues in favour of the latter. An introductory treatment of the splitwidth techn ..."
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There are two schools of thought on reasoning about distributed systems: one following interleaving based semantics, and one following partialorder/graph based semantics. This paper compares these two approaches and argues in favour of the latter. An introductory treatment of the splitwidth technique is also provided. 1
Senescent Ground Tree Rewrite Systems
"... Ground Tree Rewrite Systems with State are known to have an undecidable control state reachability problem. Taking inspiration from the recent introduction of scopebounded multistack pushdown systems, we define Senescent Ground Tree Rewrite Systems. These are a restriction of ground tree rewrite ..."
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Ground Tree Rewrite Systems with State are known to have an undecidable control state reachability problem. Taking inspiration from the recent introduction of scopebounded multistack pushdown systems, we define Senescent Ground Tree Rewrite Systems. These are a restriction of ground tree rewrite systems with state such that nodes of the tree may no longer be rewritten after having witnessed an a priori fixed number of control state changes. As well as generalising scopebounded multistack pushdown systems, we show — via reductions to and from reset Petrinets — that these systems have an Ackermanncomplete control state reachability problem. However, reachability of a regular set of trees remains undecidable.
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.