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Undirected STConnectivity in LogSpace
, 2004
"... We present a deterministic, logspace algorithm that solves stconnectivity in undirected graphs. The previous bound on the space complexity of undirected stconnectivity was log 4/3 (·) obtained by Armoni, TaShma, Wigderson and Zhou [ATSWZ00]. As undirected stconnectivity is complete for the clas ..."
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Cited by 167 (3 self)
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We present a deterministic, logspace algorithm that solves stconnectivity in undirected graphs. The previous bound on the space complexity of undirected stconnectivity was log 4/3 (·) obtained by Armoni, TaShma, Wigderson and Zhou [ATSWZ00]. As undirected stconnectivity is complete for the class of problems solvable by symmetric, nondeterministic, logspace computations (the class SL), this algorithm implies that SL = L (where L is the class of problems solvable by deterministic logspace computations). Our algorithm also implies logspace constructible universaltraversal sequences for graphs with restricted labelling and logspace constructible universalexploration sequences for general graphs.
Reasoning about Systems with Many Processes
 Journal of the ACM
, 1992
"... Abstract. Methods are given for automatically verifying temporal properties of concurrent systems containing an arbitrary number of finitestate processes that communicate using CCS actions. Two models of systems are considered. Systems in the first model consist of a unique contro [ process and an ..."
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Cited by 167 (2 self)
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Abstract. Methods are given for automatically verifying temporal properties of concurrent systems containing an arbitrary number of finitestate processes that communicate using CCS actions. Two models of systems are considered. Systems in the first model consist of a unique contro [ process and an arbitrary number of user processes with identical detlnitions, For this model, a decision procedure to check whether all the executions of a process satisfy a given specification is presented. This algorithm runs in time double exponential mthe sizes of the control andthe user process definitions. It is also proven that it is decidable whether all the fair executions of a process satisfy a gwen specification. The second model is a special case of the first. In this model, all the processes have identical definitions. For this model, an efficient decision procedure is presented that checks if every execution of a process satisfies a given temporal logic specification. This algorithm runs in time polynomial inthesize of the process definition. Itisshown howtoverify certamglobal properties such as mutual exchrslon and absence of deadlocks. Finally, it is shown how these decision procedures can beusedto reason about certain systems with a communication network,
Resolve and Expand
 In Proc. of SAT’04
, 2004
"... Abstract. We present a novel expansion based decision procedure for quantified boolean formulas (QBF) in conjunctive normal form (CNF). The basic idea is to resolve existentially quantified variables and eliminate universal variables by expansion. This process is continued until the formula becomes ..."
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Cited by 132 (18 self)
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Abstract. We present a novel expansion based decision procedure for quantified boolean formulas (QBF) in conjunctive normal form (CNF). The basic idea is to resolve existentially quantified variables and eliminate universal variables by expansion. This process is continued until the formula becomes propositional and can be solved by any SAT solver. On structured problems our implementation quantor is competitive with stateoftheart QBF solvers based on DPLL. It is orders of magnitude faster on certain hard to solve instances. 1
On relating time and space to size and depth
 SIAM Journal on Computing
, 1977
"... Abstract. Turing machine space complexity is related to circuit depth complexity. The relationship complements the known connection between Turing machine time and circuit size, thus enabling us to expose the related nature of some important open problems concerning Turing machine and circuit comple ..."
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Cited by 112 (1 self)
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Abstract. Turing machine space complexity is related to circuit depth complexity. The relationship complements the known connection between Turing machine time and circuit size, thus enabling us to expose the related nature of some important open problems concerning Turing machine and circuit complexity. We are also able to show some connection between Turing machine complexity and arithmetic complexity.
Rewriting of Regular Expressions and Regular Path Queries
, 2002
"... Recent work on semistructured data has revitalized the interest in path queries, i.e., queries that ask for all pairs of objects in the database that are connected by a path conforming to a certain specification, in particular to a regular expression. Also, in semistructured data, as well as in da ..."
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Cited by 101 (31 self)
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Recent work on semistructured data has revitalized the interest in path queries, i.e., queries that ask for all pairs of objects in the database that are connected by a path conforming to a certain specification, in particular to a regular expression. Also, in semistructured data, as well as in data integration, data warehousing, and query optimization, the problem of viewbased query rewriting is receiving much attention: Given a query and a collection of views, generate a new query which uses the views and provides the answer to the original one. In this paper we address the problem of viewbased query rewriting in the context of semistructured data. We present a method for computing the rewriting of a regular expression E in terms of other regular expressions. The method computes the exact rewriting (the one that defines the same regular language as E) if it exists, or the rewriting that defines the maximal language contained in the one defined by E, otherwise. We present a complexity analysis of both the problem and the method, showing that the latter is essentially optimal. Finally, we illustrate how to exploit the method for viewbased rewriting of regular path queries in semistructured data. The complexity results established for the rewriting of regular expressions apply also to the case of regular path queries.
Reachability is harder for directed than for undirected finite graphs
 Journal of Symbolic Logic
, 1990
"... Abstract. Although it is known that reachability in undirected finite graphs can be expressed by an existential monadic secondorder sentence, our main result is that this is not the case for directed finite graphs (even in the presence of certain “builtin ” relations, such as the successor relatio ..."
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Cited by 77 (8 self)
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Abstract. Although it is known that reachability in undirected finite graphs can be expressed by an existential monadic secondorder sentence, our main result is that this is not the case for directed finite graphs (even in the presence of certain “builtin ” relations, such as the successor relation). The proof makes use of EhrenfeuchtFrai’sse games, along with probabilistic arguments. However, we show that for directed finite graphs with degree at most k, reachability is expressible by an existential monadic secondorder sentence. $1. Introduction. If s and t denote distinguished points in a directed (resp. undirected) graph, then we say that a graph is (s, t)connected if there is a directed (undirected) path from s to t. We sometimes refer to the problem of deciding whether a given directed (undirected) graph with two given points sand t is (s, t)connected as the directed (undirected) reachability problem.
The computational Complexity of Knot and Link Problems
 J. ACM
, 1999
"... We consider the problem of deciding whether a polygonal knot in 3dimensional Euclidean space is unknotted, capable of being continuously deformed without selfintersection so that it lies in a plane. We show that this problem, unknotting problem is in NP. We also consider the problem, unknotting pr ..."
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Cited by 75 (9 self)
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We consider the problem of deciding whether a polygonal knot in 3dimensional Euclidean space is unknotted, capable of being continuously deformed without selfintersection so that it lies in a plane. We show that this problem, unknotting problem is in NP. We also consider the problem, unknotting problem of determining whether two or more such polygons can be split, or continuously deformed without selfintersection so that they occupy both sides of a plane without intersecting it. We show that it also is in NP. Finally, we show that the problem of determining the genus of a polygonal knot (a generalization of the problem of determining whether it is unknotted) is in PSPACE. We also give exponential worstcase running time bounds for deterministic algorithms to solve each of these problems. These algorithms are based on the use of normal surfaces and decision procedures due to W. Haken, with recent extensions by W. Jaco and J. L. Tollefson.
Reasoning with Concrete Domains
, 1999
"... Description logics are formalisms for the representation of and reasoning about conceptual knowledge on an abstract level. Concrete domains allow the integration of description logic reasoning with reasoning about concrete objects such as numbers, time intervals, or spatial regions. The importa ..."
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Cited by 65 (11 self)
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Description logics are formalisms for the representation of and reasoning about conceptual knowledge on an abstract level. Concrete domains allow the integration of description logic reasoning with reasoning about concrete objects such as numbers, time intervals, or spatial regions. The importance of this combined approach, especially for building realworld applications, is widely accepted. However, the complexity of reasoning with concrete domains has never been formally analyzed and efficient algorithms have not been developed. This paper closes the gap by providing a tight bound for the complexity of reasoning with concrete domains and presenting optimal algorithms. 1 Introduction Description logics are knowledge representation and reasoning formalisms dealing with conceptual knowledge on an abstract logical level. However, for a variety of applications, it is essential to integrate the abstract knowledge with knowledge of a more concrete nature. Examples of such "co...