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20
Complexity of Patternbased Verification for Multithreaded Programs
, 2011
"... Patternbased verification checks the correctness of the program executions that follow a given pattern, a regular expression over the alphabet of program transitions of the form w ∗ 1... w ∗ n. For multithreaded programs, the alphabet of the pattern is given by the synchronization operations betwee ..."
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Cited by 14 (4 self)
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Patternbased verification checks the correctness of the program executions that follow a given pattern, a regular expression over the alphabet of program transitions of the form w ∗ 1... w ∗ n. For multithreaded programs, the alphabet of the pattern is given by the synchronization operations between threads. We study the complexity of patternbased verification for abstracted multithreaded programs in which, as usual in program analysis, conditions have been replaced by nondeterminism (the technique works also for boolean programs). While unrestricted verification is undecidable for abstracted multithreaded programs with recursive procedures and PSPACEcomplete for abstracted multithreaded whileprograms, we show that patternbased verification is NPcomplete for both classes. We then conduct a multiparameter analysis in which we study the complexity in the number of threads, the number of procedures per thread, the size of the procedures, and the size of the pattern. We first show that no algorithm for patternbased verification can be polynomial in the number of threads, procedures per thread, or the size of the pattern (unless P=NP). Then, using recent results about Parikh images of regular languages and semilinear sets, we present an algorithm exponential in the number of threads, procedures per thread, and size of the pattern, but polynomial in the size of the procedures.
Simple Schemas for Unordered XML
"... We consider unordered XML, where the relative order among siblings is ignored, and propose two simple yet practical schema formalisms: disjunctive multiplicity schemas (DMS), and its restriction, disjunctionfree multiplicity schemas (MS). We investigate their computational properties and characteri ..."
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We consider unordered XML, where the relative order among siblings is ignored, and propose two simple yet practical schema formalisms: disjunctive multiplicity schemas (DMS), and its restriction, disjunctionfree multiplicity schemas (MS). We investigate their computational properties and characterize the complexity of the following static analysis problems: schema satisfiability, membership of a tree to the language of a schema, schema containment, twig query satisfiability, implication, and containment in the presence of schema. Our research indicates that the proposed formalisms retain much of the expressiveness of DTDs without an increase in computational complexity. 1.
Putting Newton into Practice: A Solver for Polynomial Equations over Semirings ⋆
"... Abstract. We present the first implementation of Newton’s method for solving systems of equations over ωcontinuous semirings (based on [5,11]). For instance, such equation systems arise naturally in the analysis of interprocedural programs or the provenance computation for Datalog. Our implementati ..."
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Cited by 3 (2 self)
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Abstract. We present the first implementation of Newton’s method for solving systems of equations over ωcontinuous semirings (based on [5,11]). For instance, such equation systems arise naturally in the analysis of interprocedural programs or the provenance computation for Datalog. Our implementation provides an attractive alternative for computing their exact least solution in some cases where the ascending chain condition is not met and hence, standard fixedpoint iteration needs to be combined with some overapproximation (e.g., widening techniques) to terminate. We present a generic C++ library along with the main algorithms and analyze their complexity. Furthermore, we describe our implementation of the counting semiring based on semilinear sets. Finally, we discuss motivating examples as well as performance benchmarks. 1
The Complexity of ReversalBounded ModelChecking ⋆
"... Abstract. We study modelchecking problems on counter systems when guards are quantifierfree Presburger formulae, the specification languages are LTLlike dialects with arithmetical constraints and the runs are restricted to reversalbounded ones. We introduce a generalization of reversalboundedne ..."
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Abstract. We study modelchecking problems on counter systems when guards are quantifierfree Presburger formulae, the specification languages are LTLlike dialects with arithmetical constraints and the runs are restricted to reversalbounded ones. We introduce a generalization of reversalboundedness and we show the NExpTimecompleteness of the reversalbounded modelchecking problem as well as for related reversalbounded reachability problems. As a byproduct, we show the effective Presburger definability for sets of configurations for which there is a reversalbounded run verifying a given temporal formula. Our results generalize existing results about reversalbounded counter automata and provides a uniform and more general framework. 1
Validating RDF with shape expressions
 CoRR
"... We propose shape expression schema (ShEx), a novel schema formalism for describing the topology of an RDF graph that uses regular bag expressions (RBEs) to define constraints on the admissible neighborhood for the nodes of a given type. We provide two alternative semantics, multi and singletype, ..."
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We propose shape expression schema (ShEx), a novel schema formalism for describing the topology of an RDF graph that uses regular bag expressions (RBEs) to define constraints on the admissible neighborhood for the nodes of a given type. We provide two alternative semantics, multi and singletype, depending on whether or not a node may have more than one type. We study the expressive power of ShEx and study the complexity of the validation problem. We show that the singletype semantics is strictly more expressive than the multitype semantics, singletype validation is generally intractable and multitype validation is feasible for a small class of RBEs. To further curb the high computational complexity of validation, we propose a natural notion of determinism and show that multitype validation for the class of deterministic schemas using singleoccurrence regular bag expressions (SORBEs) is tractable. Finally, we consider the problem of validating only a fragment of a graph with preassigned types for some of its nodes, and argue that for deterministic ShEx using SORBEs, multitype validation can be performed efficiently and singletype validation can be performed with a single pass over the graph. 1
On Hardness of Jumbled Indexing
"... Abstract. Jumbled indexing is the problem of indexing a text T for queries that ask whether there is a substring of T matching a pattern represented as a Parikh vector, i.e., the vector of frequency counts for each character. Jumbled indexing has garnered a lot of interest in the last ..."
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Abstract. Jumbled indexing is the problem of indexing a text T for queries that ask whether there is a substring of T matching a pattern represented as a Parikh vector, i.e., the vector of frequency counts for each character. Jumbled indexing has garnered a lot of interest in the last
Integer Vector Addition Systems with States
"... Abstract. This paper studies reachability, coverability and inclusion problems for Integer Vector Addition Systems with States (ZVASS) and extensions and restrictions thereof. A ZVASS comprises a finitestate controller with a finite number of counters ranging over the integers. Although it is fo ..."
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Abstract. This paper studies reachability, coverability and inclusion problems for Integer Vector Addition Systems with States (ZVASS) and extensions and restrictions thereof. A ZVASS comprises a finitestate controller with a finite number of counters ranging over the integers. Although it is folklore that reachability in ZVASS is NPcomplete, it turns out that despite their naturalness, from a complexity point of view this class has received little attention in the literature. We fill this gap by providing an indepth analysis of the computational complexity of the aforementioned decision problems. Most interestingly, it turns out that while the addition of reset operations to ordinary VASS leads to undecidability and Ackermannhardness of reachability and coverability, respectively, they can be added to ZVASS while retaining NPcompleteness of both coverability and reachability. 1
S.: Converting nondeterministic automata and contextfree grammars into Parikh equivalent deterministic automata
 DLT 2012. LNCS
"... Abstract. We investigate the conversion of oneway nondeterministic finite automata and contextfree grammars into Parikh equivalent oneway and twoway deterministic finite automata, from a descriptional complexity point of view. We prove that for each oneway nondeterministic automaton with n stat ..."
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Abstract. We investigate the conversion of oneway nondeterministic finite automata and contextfree grammars into Parikh equivalent oneway and twoway deterministic finite automata, from a descriptional complexity point of view. We prove that for each oneway nondeterministic automaton with n states there exist Parikh equivalent oneway and twoway deterministic automata with eO( n·lnn) and p(n) states, respectively, where p(n) is a polynomial. Furthermore, these costs are tight. In contrast, if all the words accepted by the given automaton contain at least two different letters, then a Parikh equivalent oneway deterministic automaton with a polynomial number of states can be found. Concerning contextfree grammars, we prove that for each grammar in Chomsky normal form with h variables there exist Parikh equivalent oneway and twoway deterministic automata with 2O(h
Trees in trees: is the incomplete information about a tree consistent? ∗
"... We are interested in the following problem: given a tree automaton A and an incomplete tree description P, does a tree T exist such that T is accepted by A and consistent with P? A tree description is a treelike structure which provides incomplete information about the shape of T. We show that this ..."
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We are interested in the following problem: given a tree automaton A and an incomplete tree description P, does a tree T exist such that T is accepted by A and consistent with P? A tree description is a treelike structure which provides incomplete information about the shape of T. We show that this problem can be solved in polynomial time as long as A and the set of possible arrangements that can be forced by P are fixed. We show how our result is related to an open problem in the theory of incomplete XML information.
Complexity and Expressiveness of ShEx for RDF
"... We study the expressiveness and complexity of Shape Expression Schema (ShEx), a novel schema formalism for RDF currently under development by W3C. ShEx assigns types to the nodes of an RDF graph and allows to constrain the admissible neighborhoods of nodes of a given type with regular bag expression ..."
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We study the expressiveness and complexity of Shape Expression Schema (ShEx), a novel schema formalism for RDF currently under development by W3C. ShEx assigns types to the nodes of an RDF graph and allows to constrain the admissible neighborhoods of nodes of a given type with regular bag expressions (RBEs). We formalize and investigate two alternative semantics, multiand singletype, depending on whether or not a node may have more than one type. We study the expressive power of ShEx and study the complexity of the validation problem. We show that the singletype semantics is strictly more expressive than the multitype semantics, singletype validation is generally intractable and multitype validation is feasible for a small (yet practical) subclass of RBEs. To curb the high computational complexity of validation, we propose a natural notion of determinism and show that multitype validation for the class of deterministic schemas using singleoccurrence regular bag expressions (SORBEs) is tractable.