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97
Motif Statistics
, 1999
"... We present a complete analysis of the statistics of number of occurrences of a regular expression pattern in a random text. This covers "motifs" widely used in computational biology. Our approach is based on: (i) a constructive approach to classical results in theoretical computer science (automata ..."
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Cited by 48 (4 self)
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We present a complete analysis of the statistics of number of occurrences of a regular expression pattern in a random text. This covers "motifs" widely used in computational biology. Our approach is based on: (i) a constructive approach to classical results in theoretical computer science (automata and formal language theory), in particular, the rationality of generating functions of regular languages; (ii) analytic combinatorics that is used for deriving asymptotic properties from generating functions; (iii) computer algebra for determining generating functions explicitly, analysing generating functions and extracting coefficients efficiently. We provide constructions for overlapping or nonoverlapping matches of a regular expression. A companion implementation produces multivariate generating functions for the statistics under study. A fast computation of Taylor coefficients of the generating functions then yields exact values of the moments with typical application to random t...
DLLite in the light of firstorder logic
 IN PROC. OF THE 22ND CONF. ON AI (AAAI07)
, 2007
"... The use of ontologies in various application domains, such as Data Integration, the Semantic Web, or ontologybased data management, where ontologies provide the access to large amounts of data, is posing challenging requirements w.r.t. a tradeoff between expressive power of a DL and efficiency of ..."
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Cited by 41 (24 self)
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The use of ontologies in various application domains, such as Data Integration, the Semantic Web, or ontologybased data management, where ontologies provide the access to large amounts of data, is posing challenging requirements w.r.t. a tradeoff between expressive power of a DL and efficiency of reasoning. The logics of the DLLite family were specifically designed to meet such requirements and optimized w.r.t. the data complexity of answering complex types of queries. In this paper we propose DLLitebool, an extension of DLLite with full Booleans and number restrictions, and study the complexity of reasoning in DLLitebool and its significant sublogics. We obtain our results, together with useful insights into the properties of the studied logics, by a novel reduction to the onevariable fragment of firstorder logic. We study the computational complexity of satisfiability and subsumption, and the data complexity of answering positive existential queries (which extend unions of conjunctive queries). Notably, we extend the LOGSPACE upper bound for the data complexity of answering unions of conjunctive queries in DLLite to positive queries and to the possibility of expressing also number restrictions, and hence local functionality in the TBox.
Modular Data Structure Verification
 EECS DEPARTMENT, MASSACHUSETTS INSTITUTE OF TECHNOLOGY
, 2007
"... This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java ..."
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Cited by 36 (21 self)
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This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java programs with dynamically allocated data structures. Developers write Jahob specifications in classical higherorder logic (HOL); Jahob reduces the verification problem to deciding the validity of HOL formulas. I present a new method for proving HOL formulas by combining automated reasoning techniques. My method consists of 1) splitting formulas into individual HOL conjuncts, 2) soundly approximating each HOL conjunct with a formula in a more tractable fragment and 3) proving the resulting approximation using a decision procedure or a theorem prover. I present three concrete logics; for each logic I show how to use it to approximate HOL formulas, and how to decide the validity of formulas in this logic. First, I present an approximation of HOL based on a translation to firstorder logic, which enables the use of existing resolutionbased theorem provers. Second, I present an approximation of HOL based on field constraint analysis, a new technique that enables
Deciding Boolean Algebra with Presburger Arithmetic
 J. of Automated Reasoning
"... Abstract. We describe an algorithm for deciding the firstorder multisorted theory BAPA, which combines 1) Boolean algebras of sets of uninterpreted elements (BA) and 2) Presburger arithmetic operations (PA). BAPA can express the relationship between integer variables and cardinalities of unbounded ..."
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Cited by 31 (26 self)
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Abstract. We describe an algorithm for deciding the firstorder multisorted theory BAPA, which combines 1) Boolean algebras of sets of uninterpreted elements (BA) and 2) Presburger arithmetic operations (PA). BAPA can express the relationship between integer variables and cardinalities of unbounded finite sets, and supports arbitrary quantification over sets and integers. Our original motivation for BAPA is deciding verification conditions that arise in the static analysis of data structure consistency properties. Data structures often use an integer variable to keep track of the number of elements they store; an invariant of such a data structure is that the value of the integer variable is equal to the number of elements stored in the data structure. When the data structure content is represented by a set, the resulting constraints can be captured in BAPA. BAPA formulas with quantifier alternations arise when verifying programs with annotations containing quantifiers, or when proving simulation relation conditions for refinement and equivalence of program fragments. Furthermore, BAPA constraints can be used for proving the termination of programs that manipulate data structures, as well as
Towards efficient satisfiability checking for boolean algebra with presburger arithmetic
 In CADE21
, 2007
"... 1 Introduction This paper considers the satisfiability problem for a logic that allows reasoning about sets and their cardinalities. We call this logic quantifierfree Boolean Algebra with Presburger Arithmetic and denote it QFBAPA. Our motivationfor QFBAPA is proving the validity of formulas arisi ..."
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Cited by 28 (17 self)
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1 Introduction This paper considers the satisfiability problem for a logic that allows reasoning about sets and their cardinalities. We call this logic quantifierfree Boolean Algebra with Presburger Arithmetic and denote it QFBAPA. Our motivationfor QFBAPA is proving the validity of formulas arising from program verification [12,13,14], but
Fast String Correction with LevenshteinAutomata
 INTERNATIONAL JOURNAL OF DOCUMENT ANALYSIS AND RECOGNITION
, 2002
"... The Levenshteindistance between two words is the minimal number of insertions, deletions or substitutions that are needed to transform one word into the other. Levenshteinautomata of degree n for a word W are defined as finite state automata that regognize the set of all words V where the Levensht ..."
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Cited by 27 (4 self)
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The Levenshteindistance between two words is the minimal number of insertions, deletions or substitutions that are needed to transform one word into the other. Levenshteinautomata of degree n for a word W are defined as finite state automata that regognize the set of all words V where the Levenshteindistance between V and W does not exceed n. We show how to compute, for any fixed bound n and any input word W , a deterministic Levenshteinautomaton of degree n for W in time linear in the length of W . Given an electronic dictionary that is implemented in the form of a trie or a finite state automaton, the Levenshteinautomaton for W can be used to control search in the lexicon in such a way that exactly the lexical words V are generated where the Levenshteindistance between V and W does not exceed the given bound. This leads to a very fast method for correcting corrupted input words of unrestricted text using large electronic dictionaries. We then introduce a second method that avoids the explicit computation of Levenshteinautomata and leads to even improved eciency. We also describe how to extend both methods to variants of the Levenshteindistance where further primitive edit operations (transpositions, merges and splits) may be used.
Reasoning over Extended ER Models
 PROCEEDINGS OF ER 2007
, 2007
"... Abstract. We investigate the computational complexity of reasoning over various fragments of the Extended EntityRelationship (EER) language, which includes a number of constructs: ISA between entities and relationships, disjointness and covering of entities and relationships, cardinality constraint ..."
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Cited by 26 (11 self)
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Abstract. We investigate the computational complexity of reasoning over various fragments of the Extended EntityRelationship (EER) language, which includes a number of constructs: ISA between entities and relationships, disjointness and covering of entities and relationships, cardinality constraints for entities in relationships and their refinements as well as multiplicity constraints for attributes. We extend the known EXPTIMEcompleteness result for UML class diagrams [5] and show that reasoning over EER diagrams with ISA between relationships is EXPTIMEcomplete even without relationship covering. Surprisingly, reasoning becomes NPcomplete when we drop ISA between relationships (while still allowing all types of constraints on entities). If we further omit disjointness and covering over entities, reasoning becomes polynomial. Our lower complexity bound results are proved by direct reductions, while the upper bounds follow from the correspondences with expressive variants of the description logic DLLite, which we establish in this paper. These correspondences also show the usefulness of DLLite as a language for reasoning over conceptual models and ontologies.
Ontologies and databases: The DLLite approach
 In Reasoning Web, volume 5689 of LNCS
, 2009
"... Abstract. Ontologies provide a conceptualization of a domain of interest. Nowadays, they are typically represented in terms of Description Logics (DLs), and are seen as the key technology used to describe the semantics of information at various sites. The idea of using ontologies as a conceptual vie ..."
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Cited by 26 (17 self)
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Abstract. Ontologies provide a conceptualization of a domain of interest. Nowadays, they are typically represented in terms of Description Logics (DLs), and are seen as the key technology used to describe the semantics of information at various sites. The idea of using ontologies as a conceptual view over data repositories is becoming more and more popular, but for it to become widespread in standard applications, it is fundamental that the conceptual layer through which the underlying data layer is accessed does not introduce a significant overhead in dealing with the data. Based on these observations, in recent years a family of DLs, called DLLite, has been proposed, which is specifically tailored to capture basic ontology and conceptual data modeling languages, while keeping low complexity of reasoning and of answering complex queries, in particular when the complexity is measured w.r.t. the size of the data. In this article, we present a detailed account of the major results that have been achieved for the DLLite family. Specifically, we concentrate on DLLiteA,id, an expressive member of this family, present algorithms for reasoning and query answering over DLLiteA,id ontologies,
Automata on guarded strings and applications
 Matématica Contemporânea
, 2001
"... Guarded strings are like ordinary strings over a finite alphabet P, except that atoms of the free Boolean algebra on a set of atomic tests B alternate with the symbols of P. The regular sets of guarded strings play the same role in Kleene algebra with tests as the regular sets of ordinary strings do ..."
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Cited by 15 (5 self)
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Guarded strings are like ordinary strings over a finite alphabet P, except that atoms of the free Boolean algebra on a set of atomic tests B alternate with the symbols of P. The regular sets of guarded strings play the same role in Kleene algebra with tests as the regular sets of ordinary strings do in Kleene algebra. In this paper we develop the elementary theory of finite automata on guarded strings, a generalization of the theory of finite automata on ordinary strings. We give several basic constructions, including determinization, state minimization, and an analog of Kleene’s theorem. We then use these results to verify a conjecture on the complexity of a complete Gentzenstyle sequent calculus for partial correctness. We also show that a basic result of the theory of Boolean decision diagrams (BDDs), namely that minimal ordered BDDs are unique, is a special case of the MyhillNerode theorem for a class of automata on guarded strings. 1
Kleene algebra with tests and program schematology
, 2001
"... The theory of flowchart schemes has a rich history going back to Ianov [6]; see Manna [22] for an elementary exposition. A central question in the theory of program schemes is scheme equivalence. Manna presents several examples of equivalence proofs that work by simplifying the schemes using various ..."
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Cited by 15 (6 self)
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The theory of flowchart schemes has a rich history going back to Ianov [6]; see Manna [22] for an elementary exposition. A central question in the theory of program schemes is scheme equivalence. Manna presents several examples of equivalence proofs that work by simplifying the schemes using various combinatorial transformation rules. In this paper we present a purely algebraic approach to this problem using Kleene algebra with tests (KAT). Instead of transforming schemes directly using combinatorial graph manipulation, we regard them as a certain kind of automaton on abstract traces. We prove a generalization of Kleene’s theorem and use it to construct equivalent expressions in the language of KAT. We can then give a purely equational proof of the equivalence of the resulting expressions. We prove soundness of the method and give a detailed example of its use. 1