Results 1  10
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241
Monotone Complexity
, 1990
"... We give a general complexity classification scheme for monotone computation, including monotone spacebounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a simple ..."
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Cited by 2837 (11 self)
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We give a general complexity classification scheme for monotone computation, including monotone spacebounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a simple notion of monotone reducibility and exhibit complete problems. This provides a framework for stating existing results and asking new questions. We show that mNL (monotone nondeterministic logspace) is not closed under complementation, in contrast to Immerman's and Szelepcs 'enyi's nonmonotone result [Imm88, Sze87] that NL = coNL; this is a simple extension of the monotone circuit depth lower bound of Karchmer and Wigderson [KW90] for stconnectivity. We also consider mBWBP (monotone bounded width branching programs) and study the question of whether mBWBP is properly contained in mNC 1 , motivated by Barrington's result [Bar89] that BWBP = NC 1 . Although we cannot answer t...
Complexity and Expressive Power of Logic Programming
, 1997
"... This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results ..."
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Cited by 360 (57 self)
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This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming. The complexity of the unification problem is also addressed.
Nondeterministic Space is Closed Under Complementation
, 1988
"... this paper we show that nondeterministic space s(n) is closed under complementation, for s(n) greater than or equal to log n. It immediately follows that the contextsensitive languages are closed under complementation, thus settling a question raised by Kuroda in 1964 [9]. See Hartmanis and Hunt [4 ..."
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Cited by 262 (14 self)
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this paper we show that nondeterministic space s(n) is closed under complementation, for s(n) greater than or equal to log n. It immediately follows that the contextsensitive languages are closed under complementation, thus settling a question raised by Kuroda in 1964 [9]. See Hartmanis and Hunt [4] for a discussion of the history and importance of this problem, and Hopcroft and Ullman [5] for all relevant background material and definitions. The history behind the proof is as follows. In 1981 we showed that the set of firstorder inductive definitions over finite structures is closed under complementation [6]. This holds with or without an ordering relation on the structure. If an ordering is present the resulting class is P. Many people expected that the result was false in the absence of an ordering. In 1983 we studied firstorder logic, with ordering, with a transitive closure operator. We showed that NSPACE[log n] is equal to (FO + pos TC), i.e. firstorder logic with ordering, plus a transitive closure operation, in which the transitive closure operator does not appear within any negation symbols [7]. Now we have returned to the issue of complementation in the light of recent results on the collapse of the log space hierarchies [10, 2, 14]. We have shown that the class (FO + pos TC) is closed under complementation. Our
A New RecursionTheoretic Characterization Of The Polytime Functions
 COMPUTATIONAL COMPLEXITY
, 1992
"... We give a recursiontheoretic characterization of FP which describes polynomial time computation independently of any externally imposed resource bounds. In particular, this syntactic characterization avoids the explicit size bounds on recursion (and the initial function 2 xy ) of Cobham. ..."
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Cited by 232 (7 self)
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We give a recursiontheoretic characterization of FP which describes polynomial time computation independently of any externally imposed resource bounds. In particular, this syntactic characterization avoids the explicit size bounds on recursion (and the initial function 2 xy ) of Cobham.
GraphLog: a Visual Formalism for Real Life Recursion
 In Proceedings of the Ninth ACM SIGACTSIGMOD Symposium on Principles of Database Systems
, 1990
"... We present a query language called GraphLog, based on a graph representation of both data and queries. Queries are graph patterns. Edges in queries represent edges or paths in the database. Regular expressions are used to qualify these paths. We characterize the expressive power of the language a ..."
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Cited by 201 (18 self)
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We present a query language called GraphLog, based on a graph representation of both data and queries. Queries are graph patterns. Edges in queries represent edges or paths in the database. Regular expressions are used to qualify these paths. We characterize the expressive power of the language and show that it is equivalent to stratified linear Datalog, first order logic with transitive closure, and nondeterministic logarithmic space (assuming ordering on the domain). The fact that the latter three classes coincide was not previously known. We show how GraphLog can be extended to incorporate aggregates and path summarization, and describe briefly our current prototype implementation. 1 Introduction The literature on theoretical and computational aspects of deductive databases, and the additional power they provide in defining and querying data, has grown rapidly in recent years. Much less work has gone into the design of languages and interfaces that make this additional pow...
On optimal lower bound on the number of variables for graph identification
 Combinatorica
, 1992
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UnQL: A Query Language and Algebra for Semistructured Data Based on Structural Recursion
, 2000
"... This paper presents structural recursion as the basis of the syntax and semantics of query languages for semistructured data and XML. We describe a simple and powerful query language based on pattern matching and show that it can be expressed using structural recursion, which is introduced as a top ..."
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Cited by 138 (4 self)
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This paper presents structural recursion as the basis of the syntax and semantics of query languages for semistructured data and XML. We describe a simple and powerful query language based on pattern matching and show that it can be expressed using structural recursion, which is introduced as a topdown, recursive function, similar to the way XSL is defined on XML trees. On cyclic data, structural recursion can be defined in two equivalent ways: as a recursive function which evaluates the data topdown and remembers all its calls to avoid infinite loops, or as a bulk evaluation which processes the entire data in parallel using only traditional relational algebra operators. The latter makes it possible for optimization techniques in relational queries to be applied to structural recursion. We show that the composition of two structural recursion queries can be expressed as a single such query, and this is used as the basis of an optimization method for mediator systems. Several other fo...
A Query Language for a WebSite Management System
 SIGMOD Record
, 1997
"... ", "Author". In addition it constructs a special node Authors() and connects it to all pages corresponding to "Author"s. The output graph is called SiteGraph. One way to write this in StruQL is: input DataGraph where Root(x); x ! ! y; y ! l ! z; l in f"Paper", &q ..."
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Cited by 111 (10 self)
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", "Author". In addition it constructs a special node Authors() and connects it to all pages corresponding to "Author"s. The output graph is called SiteGraph. One way to write this in StruQL is: input DataGraph where Root(x); x ! ! y; y ! l ! z; l in f"Paper", "TechReport", "Title", "Abstract", "Author"g create Authors(); Page(y); Page(z) link Page(y) ! l ! Page(z) where x ! ! y1; y1 ! "Author" ! z1 link Authors() ! "Author" ! Page(z1) output SiteGraph 2 In order to integrate information from several source, we allow multiple input graphs. When multiple input graphs are present, every occurrence of a collection needs to be preceded by a graph name. For clarity of presentation however, we focus on queries with only one input graph. Intermixing the where; create; link clauses makes the query easier to read. This is nothing more than syntactic convenience, since the meaning is the same as that of the query in which all clauses are joined together: input DataGraph where Root(x...
Describing Graphs: a FirstOrder Approach to Graph Canonization
, 1990
"... In this paper we ask the question, "What must be added to firstorder logic plus leastfixed point to obtain exactly the polynomialtime properties of unordered graphs?" We consider the languages Lk consisting of firstorder logic restricted to k variables and Ck consisting of Lk plus ..."
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Cited by 73 (7 self)
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In this paper we ask the question, "What must be added to firstorder logic plus leastfixed point to obtain exactly the polynomialtime properties of unordered graphs?" We consider the languages Lk consisting of firstorder logic restricted to k variables and Ck consisting of Lk plus "counting quantifiers". We give efficient canonization algorithms for graphs characterized by Ck or Lk . It follows from known results that all trees and almost all graphs are characterized by C2 .