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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 283 (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.
The Exact Computation Paradigm
, 1994
"... We describe a paradigm for numerical computing, based on exact computation. This emerging paradigm has many advantages compared to the standard paradigm which is based on fixedprecision. We first survey the literature on multiprecision number packages, a prerequisite for exact computation. Next ..."
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Cited by 94 (10 self)
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We describe a paradigm for numerical computing, based on exact computation. This emerging paradigm has many advantages compared to the standard paradigm which is based on fixedprecision. We first survey the literature on multiprecision number packages, a prerequisite for exact computation. Next we survey some recent applications of this paradigm. Finally, we outline some basic theory and techniques in this paradigm. 1 This paper will appear as a chapter in the 2nd edition of Computing in Euclidean Geometry, edited by D.Z. Du and F.K. Hwang, published by World Scientific Press, 1994. 1 1 Two Numerical Computing Paradigms Computation has always been intimately associated with numbers: computability theory was early on formulated as a theory of computable numbers, the first computers have been number crunchers and the original massproduced computers were pocket calculators. Although one's first exposure to computers today is likely to be some nonnumerical application, numeri...
Log Auditing through ModelChecking
 In Proceedings from the 14th IEEE Computer Security Foundations Workshop (CSFW’01
, 2001
"... Log auditing is a basic intrusion detection mechanism, whereby attacks are detected by uncovering matches of sequences of events against signatures. We argue that this problem is naturally expressed as a modelchecking problem against linear Kripke models. A variant of the classic linear time tempor ..."
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Cited by 32 (3 self)
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Log auditing is a basic intrusion detection mechanism, whereby attacks are detected by uncovering matches of sequences of events against signatures. We argue that this problem is naturally expressed as a modelchecking problem against linear Kripke models. A variant of the classic linear time temporal logic of Manna and Pnueli with firstorder variables is first investigated in this framework. In passing, we show that modelchecking this logic against linear models is NPcomplete  polynomialtime in the propositional case , which contrasts with the fact that it is PSPACEcomplete against general models. Despite this improvement, this logic is in dire need of refinement, as far as expressiveness and efficiency are concerned. We therefore propose a second, less standard logic consisting of flat, Wolperstyle lineartime formulae. We describe an efficient online algorithm, making the approach attractive for complex log auditing tasks. We present a few optimizations that the use of a formal semantics affords us, using abstract interpretation techniques, and report briefly on preliminary practical experience.
Deciding Provability of Linear Logic Formulas
 Advances in Linear Logic
, 1994
"... Introduction There are many interesting fragments of linear logic worthy of study in their own right, most described by the connectives which they employ. Full linear logic includes all the logical connectives, which come in three dual pairs: the exponentials ! and ?, the additives & and \Phi, and ..."
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Cited by 21 (0 self)
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Introduction There are many interesting fragments of linear logic worthy of study in their own right, most described by the connectives which they employ. Full linear logic includes all the logical connectives, which come in three dual pairs: the exponentials ! and ?, the additives & and \Phi, and the multiplicatives\Omega and . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........ . SRI International Computer Science Laboratory, Menlo Park CA 94025 USA. Work supported under NSF Grant CCR9224858. lincoln@csl.sri.com http://www.csl.sri.com/lincoln/lincoln.html Patrick Lincoln For the most part we will consider fragments of linear logic built up using these connectives in any combination. For example, full linear logic formulas may employ any connective, while multiplic
Linear Logic and Computation: A Survey
 Proof and Computation, Proceedings Marktoberdorf Summer School
, 1993
"... . This is a survey of computational aspects of linear logic related to proof search. Keywords. Linear logic, cut free proof search, logic programming, complexity. 1 Introduction Linear logic, introduced by Girard [14, 36, 32], is a refinement of classical logic. While the central notions of truth ..."
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Cited by 16 (6 self)
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. This is a survey of computational aspects of linear logic related to proof search. Keywords. Linear logic, cut free proof search, logic programming, complexity. 1 Introduction Linear logic, introduced by Girard [14, 36, 32], is a refinement of classical logic. While the central notions of truth (emphasized in classical logic) and proof construction (emphasized in intuitionistic logic) remain important in linear logic, it might be said that the emphasis in linear logic is on state. Linear logic is sometimes described as being resource sensitive because it provides an intrinsic and natural accounting of process states, events, and resources. Linear logic also sheds new light on classical logic and its relationship to intuitionistic logic, see Girard [15, 16] and Danos et al. [11]. An evocative semantic paradigm for linear logic by means of games is proposed by Blass [7] and by Abramsky and Jagadeesan [2]. As an intuitive motivation, let us consider reading logical deductions so tha...
First Order Linear Logic without Modalities Is NEXPTIMEHard
 Theoretical Computer Science
, 1994
"... The decision problem is studied for the nonmodal or multiplicativeadditive fragment of first order linear logic. This fragment is shown to be nexptime hard. The hardness proof combines Shapiro's logic programming simulation of nondeterministic Turing machines with the standard proof of the pspace ..."
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Cited by 15 (11 self)
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The decision problem is studied for the nonmodal or multiplicativeadditive fragment of first order linear logic. This fragment is shown to be nexptime hard. The hardness proof combines Shapiro's logic programming simulation of nondeterministic Turing machines with the standard proof of the pspace hardness of quantified boolean formula validity, utilizing some of the surprisingly powerful and expressive machinery of linear logic. 1 Introduction Linear logic, introduced by Girard, is a resourcesensitive refinement of classical logic [10, 29]. Linear logic gains its expressive power by restricting the "structural" proof rules of contraction (copying) and weakening (erasing). The contraction rule makes it possible to reuse any stated assumption as often as desired. The weakening rule makes it possible to use dummy assumptions, i.e., it allows a deduction to be carried out without using all of the hypotheses. Because contraction and weakening together make it possible to use an assu...
Inductive Inference of Prolog Programs with Linear Data Dependency from Positive Data
 Proc. Information Modelling and Knowledge Bases V
, 1994
"... We study inductive inference of Prolog programs from positive examples of a target predicate. Shinohara showed in 1991 that the class of linear Prologs with at most m clauses is identifiable in the limit from positive data only about a target predicate. However, linear Prologs are not allowed to hav ..."
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Cited by 11 (0 self)
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We study inductive inference of Prolog programs from positive examples of a target predicate. Shinohara showed in 1991 that the class of linear Prologs with at most m clauses is identifiable in the limit from positive data only about a target predicate. However, linear Prologs are not allowed to have local variables, which are variables occurring in the body but not in the head. In this paper, we introduce another subclass of Prolog programs, called linearly covering programs, which may have local variables in a clause under some constraints on data dependencies. In linearly covering programs, any data passing among subgoals preserves the total size of data contents. We prove that for every fixed k; m ? 0, the class of linearly covering programs consisting of at most m definite clauses with at most k subgoals in the body is inferable from positive examples of a target predicate. Furthermore, we show that the restriction on the length of bodies is necessary the inferability. 1 Introduct...
Grammar Induction as Substructural Inductive Logic Programming
 In Proceedings of the workshop on Learning Language in Logic (LLL99
, 1999
"... In this paper we describe an approach to grammar induction based on categorial grammars: the EMILE algorithm. Categorial grammars are equivalent to contextfree grammars. They were introduced by Ajduciewicz and formalised by Lambek. Technically they can be seen as a variant of the propositional ca ..."
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Cited by 4 (1 self)
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In this paper we describe an approach to grammar induction based on categorial grammars: the EMILE algorithm. Categorial grammars are equivalent to contextfree grammars. They were introduced by Ajduciewicz and formalised by Lambek. Technically they can be seen as a variant of the propositional calculus without structural rules. Various learnability results for categorial grammars are known. There exists a whole landscape of these so called substructural logics. This suggests an extension of the ILP research program in the direction of what one might call substructural ILP. We discuss the application of substructural logic to database design and present some complexity results from the literature that suggest the feasibility of this approach. 1 Introduction In this paper we introduce the notion of substructural ILP and apply it to grammar induction. If one removes the structural rules from traditional propositional calculus one obtains the Lambek calculus, which can be interp...
The Geometry in Constraint Logic Programs
 In Position Papers for the First Workshop on Principles and Practice of Constraint Programming
, 1993
"... Many applications of constraint programming languages concern geometric domains. We propose incorporating strong algorithmic techniques from the study of geometric and algebraic algorithms into the implementation of constraint programming languages. Interesting new computational problems in computat ..."
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Cited by 3 (1 self)
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Many applications of constraint programming languages concern geometric domains. We propose incorporating strong algorithmic techniques from the study of geometric and algebraic algorithms into the implementation of constraint programming languages. Interesting new computational problems in computational geometry and computer algebra arises from such considerations. We look at what is known and what needs to be addressed.