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86
Improvements To Propositional Satisfiability Search Algorithms
, 1995
"... ... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400variable 3SAT problems in about 2 hours on the average. In general, it can solve hard nvariable ..."
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... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400variable 3SAT problems in about 2 hours on the average. In general, it can solve hard nvariable random 3SAT problems with search trees of size O(2 n=18:7 ). In addition to justifying these claims, this dissertation describes the most significant achievements of other researchers in this area, and discusses all of the widely known general techniques for speeding up SAT search algorithms. It should be useful to anyone interested in NPcomplete problems or combinatorial optimization in general, and it should be particularly useful to researchers in either Artificial Intelligence or Operations Research.
Learning conjunctions of Horn clauses
 In Proceedings of the 31st Annual Symposium on Foundations of Computer Science
, 1990
"... Abstract. An algorithm is presented for learning the class of Boolean formulas that are expressible as conjunctions of Horn clauses. (A Horn clause is a disjunction of literals, all but at most one of which is a negated variable.) The algorithm uses equivalence queries and membership queries to prod ..."
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Cited by 120 (14 self)
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Abstract. An algorithm is presented for learning the class of Boolean formulas that are expressible as conjunctions of Horn clauses. (A Horn clause is a disjunction of literals, all but at most one of which is a negated variable.) The algorithm uses equivalence queries and membership queries to produce a formula that is logically equivalent to the unknown formula to be learned. The amount of time used by the algorithm is polynomial in the number of variables and the number of clauses in the unknown formula.
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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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.
The complexity of relational query languages (extended abstract
 In Proceedings of the fourteenth annual ACM symposium on Theory of computing (STOC ’82
, 1982
"... Two complexity measures for query languages are proposed. Data complexity is the complexity of evaluating a query in the language as a function of the size of the database, and expression complexity is the complexity of ewduating a query in the language as a function of the size of the expression de ..."
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Two complexity measures for query languages are proposed. Data complexity is the complexity of evaluating a query in the language as a function of the size of the database, and expression complexity is the complexity of ewduating a query in the language as a function of the size of the expression defining the query. We study the data and expression complexity of logical langnages relational calculus and its extensions by transitive closure, fixpoint and second order existential quantification and algebraic languages relational algebra and its extensions by bounded and unbounded looping. The pattern which will bc shown is that the expression complexity of the investigated languages is one exponential higher then their data complexity, and for both types of complexity we show completeness in some complexity class. Research supported by a Weizrnann Postdoctoral Fellowship,
Models of Computation  Exploring the Power of Computing
"... Theoretical computer science treats any computational subject for which a good model can be created. Research on formal models of computation was initiated in the 1930s and 1940s by Turing, Post, Kleene, Church, and others. In the 1950s and 1960s programming languages, language translators, and oper ..."
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Cited by 85 (6 self)
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Theoretical computer science treats any computational subject for which a good model can be created. Research on formal models of computation was initiated in the 1930s and 1940s by Turing, Post, Kleene, Church, and others. In the 1950s and 1960s programming languages, language translators, and operating systems were under development and therefore became both the subject and basis for a great deal of theoretical work. The power of computers of this period was limited by slow processors and small amounts of memory, and thus theories (models, algorithms, and analysis) were developed to explore the efficient use of computers as well as the inherent complexity of problems. The former subject is known today as algorithms and data structures, the latter computational complexity. The focus of theoretical computer scientists in the 1960s on languages is reflected in the first textbook on the subject, Formal Languages and Their Relation to Automata by John Hopcroft and Jeffrey Ullman. This influential book led to the creation of many languagecentered theoretical computer science courses; many introductory theory courses today continue to reflect the content of this book and the interests of theoreticians of the 1960s and early 1970s. Although
Separation of the Monotone NC Hierarchy
, 1999
"... We prove tight lower bounds, of up to n ffl , for the monotone depth of functions in monotoneP. As a result we achieve the separation of the following classes. 1. monotoneNC 6= monotoneP. 2. For every i 1, monotoneNC i 6= monotoneNC i+1 . 3. More generally: For any integer function D( ..."
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We prove tight lower bounds, of up to n ffl , for the monotone depth of functions in monotoneP. As a result we achieve the separation of the following classes. 1. monotoneNC 6= monotoneP. 2. For every i 1, monotoneNC i 6= monotoneNC i+1 . 3. More generally: For any integer function D(n), up to n ffl (for some ffl ? 0), we give an explicit example of a monotone Boolean function, that can be computed by polynomial size monotone Boolean circuits of depth D(n), but that cannot be computed by any (fanin 2) monotone Boolean circuits of depth less than Const \Delta D(n) (for some constant Const). Only a separation of monotoneNC 1 from monotoneNC 2 was previously known. Our argument is more general: we define a new class of communication complexity search problems, referred to below as DART games, and we prove a tight lower bound for the communication complexity of every member of this class. As a result we get lower bounds for the monotone depth of many functions. In...
Interconvertibility of a Class of Set Constraints and ContextFreeLanguage Reachability
 TCS
, 1998
"... We show the interconvertibility of contextfreelanguage reachability problems and a class of setconstraint problems: given a contextfreelanguage reachability problem, we show how to construct a setconstraint problem whose answer gives a solution to the reachability problem; given a setconstra ..."
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Cited by 43 (2 self)
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We show the interconvertibility of contextfreelanguage reachability problems and a class of setconstraint problems: given a contextfreelanguage reachability problem, we show how to construct a setconstraint problem whose answer gives a solution to the reachability problem; given a setconstraint problem, we show how to construct a contextfreelanguage reachability problem whose answer gives a solution to the setconstraint problem. The interconvertibility of these two formalisms offers an conceptual advantage akin to the advantage gained from the interconvertibility of finitestate automata and regular expressions in formal language theory, namely, a problem can be formulated in whichever formalism is most natural. It also offers some insight into the "O(n ) bottleneck" for different types of programanalysis problems and allows results previously obtained for contextfreelanguage reachability problems to be applied to setconstraint problems and vice versa.
Relativization of questions about log space computability
 Mathematical Systems Theory
, 1976
"... A notion of log space Turing reducibility is introduced. It is used to define relative notions of log space, ~A, and nondeterministic log space, Jg'£ ~ A. These classes are compared with the classes ~a and JV' ~ A which were originally defined by Baker, Gill, and Solovay [BGS]. It is shown ..."
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A notion of log space Turing reducibility is introduced. It is used to define relative notions of log space, ~A, and nondeterministic log space, Jg'£ ~ A. These classes are compared with the classes ~a and JV' ~ A which were originally defined by Baker, Gill, and Solovay [BGS]. It is shown that there exists acomputable set A such that ~V' ~ a ~ ~A. Furthermore, there exists a computable set A such that jff~A d: ~a and ~a 4 =.Ar~A. Also a notion of log space truth table reducibility is defined and shown to be equivalent to the notion of log space Turing reducibility. Introduction. Reducibility in polynomial time has received wide attention, in references [C2], [K], [Lal], [LLS], [BGS] and in many other places. There are several considerations which support a similar examination of reducibility in lot space. First, unlike polynomial time reducibility, log space reducibility allows a meaningful classification of problems that are computable in polynomial time