The Experts below are selected from a list of 264 Experts worldwide ranked by ideXlab platform
Andrei Voronkov - One of the best experts on this subject based on the ideXlab platform.
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a nondeterministic polynomial time Unification Algorithm for bags sets and trees
Foundations of Software Science and Computation Structure, 1999Co-Authors: Evgeny Dantsin, Andrei VoronkovAbstract:Unification in logic programming deals with tree-like data represented by terms. Some applications, including deductive databases, require handling more complex values, for example finite sets or bags (finite multisets). We extend Unification to the combined domain of bags, sets and trees in which bags and sets are generated by constructors similar to the list constructor. Our Unification Algorithm is presented as a nondeterministic polynomial-time Algorithm that solves equality constraints in the spirit of the Martelli and Montanari Algorithm.
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FoSSaCS - A Nondeterministic Polynomial-Time Unification Algorithm for Bags, Sets and Trees
Lecture Notes in Computer Science, 1999Co-Authors: Evgeny Dantsin, Andrei VoronkovAbstract:Unification in logic programming deals with tree-like data represented by terms. Some applications, including deductive databases, require handling more complex values, for example finite sets or bags (finite multisets). We extend Unification to the combined domain of bags, sets and trees in which bags and sets are generated by constructors similar to the list constructor. Our Unification Algorithm is presented as a nondeterministic polynomial-time Algorithm that solves equality constraints in the spirit of the Martelli and Montanari Algorithm.
Evgeny Dantsin - One of the best experts on this subject based on the ideXlab platform.
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a nondeterministic polynomial time Unification Algorithm for bags sets and trees
Foundations of Software Science and Computation Structure, 1999Co-Authors: Evgeny Dantsin, Andrei VoronkovAbstract:Unification in logic programming deals with tree-like data represented by terms. Some applications, including deductive databases, require handling more complex values, for example finite sets or bags (finite multisets). We extend Unification to the combined domain of bags, sets and trees in which bags and sets are generated by constructors similar to the list constructor. Our Unification Algorithm is presented as a nondeterministic polynomial-time Algorithm that solves equality constraints in the spirit of the Martelli and Montanari Algorithm.
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FoSSaCS - A Nondeterministic Polynomial-Time Unification Algorithm for Bags, Sets and Trees
Lecture Notes in Computer Science, 1999Co-Authors: Evgeny Dantsin, Andrei VoronkovAbstract:Unification in logic programming deals with tree-like data represented by terms. Some applications, including deductive databases, require handling more complex values, for example finite sets or bags (finite multisets). We extend Unification to the combined domain of bags, sets and trees in which bags and sets are generated by constructors similar to the list constructor. Our Unification Algorithm is presented as a nondeterministic polynomial-time Algorithm that solves equality constraints in the spirit of the Martelli and Montanari Algorithm.
Wang Shu - One of the best experts on this subject based on the ideXlab platform.
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a new Algorithm of pattern Unification
Computer Science, 2006Co-Authors: Wang ShuAbstract:Traditional pattrn Unification Algorithm adopts the recursive method,which time complexity is exponential.Traditional pattern Unification Algorithm consumes so much system resourch that the system is easy to breakdown.To solve the problem,this paper proposes a new pattern Unification Algorithm,which time complexity is linear.Experiment result indicates that the new Algorithm can successfully solve the recursive problem which exists in customary Algorithm.
Lida Wang - One of the best experts on this subject based on the ideXlab platform.
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A Unification Algorithm for Analysis of Protocols with Blinded Signatures
Mechanizing Mathematical Reasoning, 2005Co-Authors: Deepak Kapur, Paliath Narendran, Lida WangAbstract:Analysis of authentication cryptographic protocols, particularly finding flaws in them and determining a sequence of actions that an intruder can take to gain access to the information which a given protocol purports not to reveal, has recently received considerable attention. One effective way of detecting flaws is to hypothesize an insecure state and determine whether it is possible to get to that state by a legal sequence of actions permitted by the protocol from some legal initial state which captures the knowledge of the principals and the assumptions made about an intruder’s behavior. Relations among encryption and decryption functions as well as properties of number theoretic functions used in encryption and decryption can be specified as rewrite rules. This, for example, is the approach used by the NRL Protocol Analyzer, which uses narrowing to reason about such properties of cryptographic and number-theoretic functions.Following [15], a related approach is proposed here in which equation solving modulo most of these properties of cryptographic and number-theoretic functions is done by developing new Unification Algorithms for such theories. A new Unification Algorithm for an equational theory needed to reason about protocols that use the Diffie-Hellman Algorithm is developed. In this theory, multiplication forms an abelian group; exponentiation function distributes over multiplication, and exponents can commute. This theory is useful for analyzing protocols which use blinded signatures. It is proved that the Unification problem over this equational theory can be reduced to the Unification problem modulo the theory of abelian groups with commuting homomorphisms with an additional constraint. Baader’s Unification Algorithm for the theory of abelian groups with commuting homomorphisms, which reduces the Unification problem to solving equations over the polynomial ring over the integers with the commuting homomorphisms serving as indeterminates, is generalized to give a Unification Algorithm over the theory of abelian groups with commuting homomorphism with a linear constraint.It is also shown that the Unification problem over a (simple) extension of the equational theory considered here (which is also an extension of the equational theory considered in [15]) is undecidable.
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Mechanizing Mathematical Reasoning - A Unification Algorithm for Analysis of Protocols with Blinded Signatures
Lecture Notes in Computer Science, 2005Co-Authors: Deepak Kapur, Paliath Narendran, Lida WangAbstract:Analysis of authentication cryptographic protocols, particularly finding flaws in them and determining a sequence of actions that an intruder can take to gain access to the information which a given protocol purports not to reveal, has recently received considerable attention. One effective way of detecting flaws is to hypothesize an insecure state and determine whether it is possible to get to that state by a legal sequence of actions permitted by the protocol from some legal initial state which captures the knowledge of the principals and the assumptions made about an intruder''s behavior. Relations among encryption and decryption functions as well as properties of number theoretic functions used in encryption and decryption can be specified as rewrite rules. This, for example, is the approach used by the NRL Protocol Analyzer, which uses narrowing to reason about such properties of cryptographic and number-theoretic functions. Following [15], a related approach is proposed here in which equation solving modulo most of these properties of cryptographic and number-theoretic functions is done by developing new Unification Algorithms for such theories. A new Unification Algorithm for an equational theory needed to reason about protocols that use the Diffie-Hellman Algorithm is developed. In this theory, multiplication forms an abelian group; exponentiation function distributes over multiplication, and exponents can commute. This theory is useful for analyzing protocols which use blinded signatures. It is proved that the Unification problem over this equational theory can be reduced to the Unification problem modulo the theory of abelian groups with commuting homomorphisms with an additional constraint. Baader''s Unification Algorithm for the theory of abelian groups with commuting homomorphisms, which reduces the Unification problem to solving equations over the polynomial ring over the integers with the commuting homomorphisms serving as indeterminates, is generalized to give a Unification Algorithm over the theory of abelian groups with commuting homomorphism with a linear constraint. It is also shown that the Unification problem over a (simple) extension of the equational theory considered here (which is also an extension of the equational theory considered in [15]) is undecidable.
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an e Unification Algorithm for analyzing protocols that use modular exponentiation
Lecture Notes in Computer Science, 2003Co-Authors: Deepak Kapur, Paliath Narendran, Lida WangAbstract:Modular multiplication and exponentiation are common operations in modern cryptography. Unification problems with respect to some equational theories that these operations satisfy are investigated. Two different but related equational theories are analyzed. A Unification Algorithm is given for one of the theories which relies on solving syzygies over multivariate integral polynomials with noncommuting indeterminates. For the other theory, in which the distributivity property of exponentiation over multiplication is assumed, the unifiability problem is shown to be undecidable by adapting a construction developed by one of the authors to reduce Hilbert's 10th problem to the solvability problem for linear equations over semi-rings. A new Algorithm for computing strong Grobner bases of right ideals over the polynomial ring Z is proposed; unlike earlier Algorithms proposed by Baader as well as by Madlener and Reinert which work only for right admissible term orderings with the boundedness property, this Algorithm works for any right admissible term ordering. The Algorithms for some of these Unification problems are expected to be integrated into Naval Research Lab.'s Protocol Analyzer (NPA), a tool developed by Catherine Meadows, which has been successfully used to analyze cryptographic protocols, particularly emerging standards such as the Internet Engineering Task Force's (IETF) Internet Key Exchange [11] and Group Domain of Interpretation [12] protocols. Techniques from several different fields - particularly symbolic computation (ideal theory and Groebner basis Algorithms) and Unification theory - are thus used to address problems arising in state-based cryptographic protocol analysis.
Deepak Kapur - One of the best experts on this subject based on the ideXlab platform.
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Hierarchical Combination
2013Co-Authors: Serdar Erbatur, Deepak Kapur, Paliath Narendran, Andrew Marshall, Christophe RingeissenAbstract:A novel approach is described for the combination of Unification Algorithms for two equational theories E 1 and E 2 which share function symbols. We are able to identify a set of restrictions and a combination method such that if the restrictions are satisfied the method produces a Unification Algorithm for the union of non-disjoint equational theories. Furthermore, we identify a class of theories satisfying the restrictions. The critical characteristics of the class is the hierarchical organization and the shared symbols being restricted to "inner constructors".
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A Unification Algorithm for Analysis of Protocols with Blinded Signatures
Mechanizing Mathematical Reasoning, 2005Co-Authors: Deepak Kapur, Paliath Narendran, Lida WangAbstract:Analysis of authentication cryptographic protocols, particularly finding flaws in them and determining a sequence of actions that an intruder can take to gain access to the information which a given protocol purports not to reveal, has recently received considerable attention. One effective way of detecting flaws is to hypothesize an insecure state and determine whether it is possible to get to that state by a legal sequence of actions permitted by the protocol from some legal initial state which captures the knowledge of the principals and the assumptions made about an intruder’s behavior. Relations among encryption and decryption functions as well as properties of number theoretic functions used in encryption and decryption can be specified as rewrite rules. This, for example, is the approach used by the NRL Protocol Analyzer, which uses narrowing to reason about such properties of cryptographic and number-theoretic functions.Following [15], a related approach is proposed here in which equation solving modulo most of these properties of cryptographic and number-theoretic functions is done by developing new Unification Algorithms for such theories. A new Unification Algorithm for an equational theory needed to reason about protocols that use the Diffie-Hellman Algorithm is developed. In this theory, multiplication forms an abelian group; exponentiation function distributes over multiplication, and exponents can commute. This theory is useful for analyzing protocols which use blinded signatures. It is proved that the Unification problem over this equational theory can be reduced to the Unification problem modulo the theory of abelian groups with commuting homomorphisms with an additional constraint. Baader’s Unification Algorithm for the theory of abelian groups with commuting homomorphisms, which reduces the Unification problem to solving equations over the polynomial ring over the integers with the commuting homomorphisms serving as indeterminates, is generalized to give a Unification Algorithm over the theory of abelian groups with commuting homomorphism with a linear constraint.It is also shown that the Unification problem over a (simple) extension of the equational theory considered here (which is also an extension of the equational theory considered in [15]) is undecidable.
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Mechanizing Mathematical Reasoning - A Unification Algorithm for Analysis of Protocols with Blinded Signatures
Lecture Notes in Computer Science, 2005Co-Authors: Deepak Kapur, Paliath Narendran, Lida WangAbstract:Analysis of authentication cryptographic protocols, particularly finding flaws in them and determining a sequence of actions that an intruder can take to gain access to the information which a given protocol purports not to reveal, has recently received considerable attention. One effective way of detecting flaws is to hypothesize an insecure state and determine whether it is possible to get to that state by a legal sequence of actions permitted by the protocol from some legal initial state which captures the knowledge of the principals and the assumptions made about an intruder''s behavior. Relations among encryption and decryption functions as well as properties of number theoretic functions used in encryption and decryption can be specified as rewrite rules. This, for example, is the approach used by the NRL Protocol Analyzer, which uses narrowing to reason about such properties of cryptographic and number-theoretic functions. Following [15], a related approach is proposed here in which equation solving modulo most of these properties of cryptographic and number-theoretic functions is done by developing new Unification Algorithms for such theories. A new Unification Algorithm for an equational theory needed to reason about protocols that use the Diffie-Hellman Algorithm is developed. In this theory, multiplication forms an abelian group; exponentiation function distributes over multiplication, and exponents can commute. This theory is useful for analyzing protocols which use blinded signatures. It is proved that the Unification problem over this equational theory can be reduced to the Unification problem modulo the theory of abelian groups with commuting homomorphisms with an additional constraint. Baader''s Unification Algorithm for the theory of abelian groups with commuting homomorphisms, which reduces the Unification problem to solving equations over the polynomial ring over the integers with the commuting homomorphisms serving as indeterminates, is generalized to give a Unification Algorithm over the theory of abelian groups with commuting homomorphism with a linear constraint. It is also shown that the Unification problem over a (simple) extension of the equational theory considered here (which is also an extension of the equational theory considered in [15]) is undecidable.
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an e Unification Algorithm for analyzing protocols that use modular exponentiation
Lecture Notes in Computer Science, 2003Co-Authors: Deepak Kapur, Paliath Narendran, Lida WangAbstract:Modular multiplication and exponentiation are common operations in modern cryptography. Unification problems with respect to some equational theories that these operations satisfy are investigated. Two different but related equational theories are analyzed. A Unification Algorithm is given for one of the theories which relies on solving syzygies over multivariate integral polynomials with noncommuting indeterminates. For the other theory, in which the distributivity property of exponentiation over multiplication is assumed, the unifiability problem is shown to be undecidable by adapting a construction developed by one of the authors to reduce Hilbert's 10th problem to the solvability problem for linear equations over semi-rings. A new Algorithm for computing strong Grobner bases of right ideals over the polynomial ring Z is proposed; unlike earlier Algorithms proposed by Baader as well as by Madlener and Reinert which work only for right admissible term orderings with the boundedness property, this Algorithm works for any right admissible term ordering. The Algorithms for some of these Unification problems are expected to be integrated into Naval Research Lab.'s Protocol Analyzer (NPA), a tool developed by Catherine Meadows, which has been successfully used to analyze cryptographic protocols, particularly emerging standards such as the Internet Engineering Task Force's (IETF) Internet Key Exchange [11] and Group Domain of Interpretation [12] protocols. Techniques from several different fields - particularly symbolic computation (ideal theory and Groebner basis Algorithms) and Unification theory - are thus used to address problems arising in state-based cryptographic protocol analysis.
