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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 113 (16 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 97 (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 90 (29 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 75 (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.
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 60 (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...
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 58 (8 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.
Two applications of inductive counting for complementation problems
 SIAM Journal of Computing
, 1989
"... nondeterministic spacebounded complexity classes are closed under complementation, two further applications of the inductive counting technique are developed. First, an errorless probabilistic algorithm for the undirected graph st connectivity problem that runs in O(log n) space and polynomial exp ..."
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Cited by 53 (3 self)
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nondeterministic spacebounded complexity classes are closed under complementation, two further applications of the inductive counting technique are developed. First, an errorless probabilistic algorithm for the undirected graph st connectivity problem that runs in O(log n) space and polynomial expected time is given. Then it is shown that the class LOGCFL is closed under complementation. The latter is a special case of a general result that shows closure under complementation of classes defined by semiunbounded fanin circuits (or, equivalently, nondeterministic auxiliary pushdown automata or treesize bounded alternating Turing machines). As one consequence, it is shown that small numbers of "role switches " in twoperson pebbling can be eliminated.