The Experts below are selected from a list of 6390 Experts worldwide ranked by ideXlab platform
Michael Luttenberger - One of the best experts on this subject based on the ideXlab platform.
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solving fixed point equations by Derivation Tree analysis
Conference on Algebra and Coalgebra in Computer Science, 2011Co-Authors: Javier Esparza, Michael LuttenbergerAbstract:Systems of equations over ω-continuous semirings can be mapped to context-free grammars in a natural way. We show how an analysis of the Derivation Trees of the grammar yields new algorithms for approximating and even computing exactly the least solution of the system.
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Derivation Tree analysis for accelerated fixed-point computation☆
Theoretical Computer Science, 2011Co-Authors: Javier Esparza, Stefan Kiefer, Michael LuttenbergerAbstract:We show that for several classes of idempotent semirings the least fixed-point of a polynomial system of equations X=f(X) is equal to the least fixed-point of a linear system obtained by “linearizing” the polynomials of f in a certain way. Our proofs rely on Derivation Tree analysis, a proof principle that combines methods from algebra, calculus, and formal language theory, and was first used in Esparza et al. (2007) [10], to show that Newton’s method over commutative and idempotent semirings converges in a linear number of steps. Our results lead to efficient generic algorithms for computing the least fixed-point. We use these algorithms to derive several consequences, including an O(N3) algorithm for computing the throughput of a context-free grammar (obtained by speeding up the O(N4) algorithm of Caucal et al. (2007) [7]), and a generalization of Courcelle’s result stating that the downward-closed image of a context-free language is regular (Courcelle, 1991) [8].
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CALCO - Solving fixed-point equations by Derivation Tree analysis
Algebra and Coalgebra in Computer Science, 2011Co-Authors: Javier Esparza, Michael LuttenbergerAbstract:Systems of equations over ω-continuous semirings can be mapped to context-free grammars in a natural way. We show how an analysis of the Derivation Trees of the grammar yields new algorithms for approximating and even computing exactly the least solution of the system.
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Derivation Tree analysis for accelerated fixed point computation
Developments in Language Theory, 2008Co-Authors: Javier Esparza, Stefan Kiefer, Michael LuttenbergerAbstract:We show that for several classes of idempotent semirings the least fixed-point of a polynomial system of equations is equal to the least fixed-point of a linearsystem obtained by "linearizing" the polynomials of in a certain way. Our proofs rely on Derivation Tree analysis, a proof principle that combines methods from algebra, calculus, and formal language theory, and was first used in [5] to show that Newton's method over commutative and idempotent semirings converges in a linear number of steps. Our results lead to efficient generic algorithms for computing the least fixed-point. We use these algorithms to derive several consequences, including an O(N3) algorithm for computing the throughput of a context-free grammar (obtained by speeding up the O(N4) algorithm of [2]), and a generalization of Courcelle's result stating that the downward-closed image of a context-free language is regular [3].
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Developments in Language Theory - Derivation Tree Analysis for Accelerated Fixed-Point Computation
Developments in Language Theory, 1Co-Authors: Javier Esparza, Stefan Kiefer, Michael LuttenbergerAbstract:We show that for several classes of idempotent semirings the least fixed-point of a polynomial system of equations is equal to the least fixed-point of a linearsystem obtained by "linearizing" the polynomials of in a certain way. Our proofs rely on Derivation Tree analysis, a proof principle that combines methods from algebra, calculus, and formal language theory, and was first used in [5] to show that Newton's method over commutative and idempotent semirings converges in a linear number of steps. Our results lead to efficient generic algorithms for computing the least fixed-point. We use these algorithms to derive several consequences, including an O(N3) algorithm for computing the throughput of a context-free grammar (obtained by speeding up the O(N4) algorithm of [2]), and a generalization of Courcelle's result stating that the downward-closed image of a context-free language is regular [3].
Javier Esparza - One of the best experts on this subject based on the ideXlab platform.
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solving fixed point equations by Derivation Tree analysis
Conference on Algebra and Coalgebra in Computer Science, 2011Co-Authors: Javier Esparza, Michael LuttenbergerAbstract:Systems of equations over ω-continuous semirings can be mapped to context-free grammars in a natural way. We show how an analysis of the Derivation Trees of the grammar yields new algorithms for approximating and even computing exactly the least solution of the system.
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Derivation Tree analysis for accelerated fixed-point computation☆
Theoretical Computer Science, 2011Co-Authors: Javier Esparza, Stefan Kiefer, Michael LuttenbergerAbstract:We show that for several classes of idempotent semirings the least fixed-point of a polynomial system of equations X=f(X) is equal to the least fixed-point of a linear system obtained by “linearizing” the polynomials of f in a certain way. Our proofs rely on Derivation Tree analysis, a proof principle that combines methods from algebra, calculus, and formal language theory, and was first used in Esparza et al. (2007) [10], to show that Newton’s method over commutative and idempotent semirings converges in a linear number of steps. Our results lead to efficient generic algorithms for computing the least fixed-point. We use these algorithms to derive several consequences, including an O(N3) algorithm for computing the throughput of a context-free grammar (obtained by speeding up the O(N4) algorithm of Caucal et al. (2007) [7]), and a generalization of Courcelle’s result stating that the downward-closed image of a context-free language is regular (Courcelle, 1991) [8].
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CALCO - Solving fixed-point equations by Derivation Tree analysis
Algebra and Coalgebra in Computer Science, 2011Co-Authors: Javier Esparza, Michael LuttenbergerAbstract:Systems of equations over ω-continuous semirings can be mapped to context-free grammars in a natural way. We show how an analysis of the Derivation Trees of the grammar yields new algorithms for approximating and even computing exactly the least solution of the system.
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Derivation Tree analysis for accelerated fixed point computation
Developments in Language Theory, 2008Co-Authors: Javier Esparza, Stefan Kiefer, Michael LuttenbergerAbstract:We show that for several classes of idempotent semirings the least fixed-point of a polynomial system of equations is equal to the least fixed-point of a linearsystem obtained by "linearizing" the polynomials of in a certain way. Our proofs rely on Derivation Tree analysis, a proof principle that combines methods from algebra, calculus, and formal language theory, and was first used in [5] to show that Newton's method over commutative and idempotent semirings converges in a linear number of steps. Our results lead to efficient generic algorithms for computing the least fixed-point. We use these algorithms to derive several consequences, including an O(N3) algorithm for computing the throughput of a context-free grammar (obtained by speeding up the O(N4) algorithm of [2]), and a generalization of Courcelle's result stating that the downward-closed image of a context-free language is regular [3].
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Developments in Language Theory - Derivation Tree Analysis for Accelerated Fixed-Point Computation
Developments in Language Theory, 1Co-Authors: Javier Esparza, Stefan Kiefer, Michael LuttenbergerAbstract:We show that for several classes of idempotent semirings the least fixed-point of a polynomial system of equations is equal to the least fixed-point of a linearsystem obtained by "linearizing" the polynomials of in a certain way. Our proofs rely on Derivation Tree analysis, a proof principle that combines methods from algebra, calculus, and formal language theory, and was first used in [5] to show that Newton's method over commutative and idempotent semirings converges in a linear number of steps. Our results lead to efficient generic algorithms for computing the least fixed-point. We use these algorithms to derive several consequences, including an O(N3) algorithm for computing the throughput of a context-free grammar (obtained by speeding up the O(N4) algorithm of [2]), and a generalization of Courcelle's result stating that the downward-closed image of a context-free language is regular [3].
Stefan Forstenlechner - One of the best experts on this subject based on the ideXlab platform.
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grammar design for Derivation Tree based genetic programming systems
European Conference on Genetic Programming, 2016Co-Authors: Stefan Forstenlechner, Miguel Nicolau, David Fagan, Michael OneillAbstract:Grammar-based genetic programming systems have gained interest in recent decades and are widely used nowadays. Although researchers normally present the grammar used to solve a certain problem, they seldom write about processes used to construct the grammar. This paper sheds some light on how to design a grammar that not only covers the search space, but also supports the search process in finding good solutions. The focus lies on context free grammar guided systems using Derivation Tree crossover and mutation, in contrast to linearised grammar based systems. Several grammars are presented encompassing the search space of sorting networks and show concepts which apply to general grammar design. An analysis of the search operators on different grammar is undertaken and performance examined on the sorting network problem. The results show that the overall structure for Derivation Trees created by the grammar has little effect on the performance, but still affects the genetic material changed by search operators.
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EuroGP - Grammar Design for Derivation Tree Based Genetic Programming Systems
Lecture Notes in Computer Science, 2016Co-Authors: Stefan Forstenlechner, Miguel Nicolau, David Fagan, Michael O'neillAbstract:Grammar-based genetic programming systems have gained interest in recent decades and are widely used nowadays. Although researchers normally present the grammar used to solve a certain problem, they seldom write about processes used to construct the grammar. This paper sheds some light on how to design a grammar that not only covers the search space, but also supports the search process in finding good solutions. The focus lies on context free grammar guided systems using Derivation Tree crossover and mutation, in contrast to linearised grammar based systems. Several grammars are presented encompassing the search space of sorting networks and show concepts which apply to general grammar design. An analysis of the search operators on different grammar is undertaken and performance examined on the sorting network problem. The results show that the overall structure for Derivation Trees created by the grammar has little effect on the performance, but still affects the genetic material changed by search operators.
David Fagan - One of the best experts on this subject based on the ideXlab platform.
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grammar design for Derivation Tree based genetic programming systems
European Conference on Genetic Programming, 2016Co-Authors: Stefan Forstenlechner, Miguel Nicolau, David Fagan, Michael OneillAbstract:Grammar-based genetic programming systems have gained interest in recent decades and are widely used nowadays. Although researchers normally present the grammar used to solve a certain problem, they seldom write about processes used to construct the grammar. This paper sheds some light on how to design a grammar that not only covers the search space, but also supports the search process in finding good solutions. The focus lies on context free grammar guided systems using Derivation Tree crossover and mutation, in contrast to linearised grammar based systems. Several grammars are presented encompassing the search space of sorting networks and show concepts which apply to general grammar design. An analysis of the search operators on different grammar is undertaken and performance examined on the sorting network problem. The results show that the overall structure for Derivation Trees created by the grammar has little effect on the performance, but still affects the genetic material changed by search operators.
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EuroGP - Grammar Design for Derivation Tree Based Genetic Programming Systems
Lecture Notes in Computer Science, 2016Co-Authors: Stefan Forstenlechner, Miguel Nicolau, David Fagan, Michael O'neillAbstract:Grammar-based genetic programming systems have gained interest in recent decades and are widely used nowadays. Although researchers normally present the grammar used to solve a certain problem, they seldom write about processes used to construct the grammar. This paper sheds some light on how to design a grammar that not only covers the search space, but also supports the search process in finding good solutions. The focus lies on context free grammar guided systems using Derivation Tree crossover and mutation, in contrast to linearised grammar based systems. Several grammars are presented encompassing the search space of sorting networks and show concepts which apply to general grammar design. An analysis of the search operators on different grammar is undertaken and performance examined on the sorting network problem. The results show that the overall structure for Derivation Trees created by the grammar has little effect on the performance, but still affects the genetic material changed by search operators.
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EuroGP - Understanding expansion order and phenotypic connectivity in πGE
Lecture Notes in Computer Science, 2013Co-Authors: David Fagan, Michael O'neill, Erik Hemberg, Seán McgarraghyAbstract:Since its inception, πGE has used evolution to guide the order of how to construct Derivation Trees. It was hypothesised that this would allow evolution to adjust the order of expansion during the run and thus help with search. This research aims to identify if a specific order is reachable, how reachable it may be, and goes on to investigate what happens to the expansion order during a πGE run. It is concluded that within πGE we do not evolve towards a specific order but a rather distribution of orders. The added complexity that an evolvable order gives πGE can make it difficult to understand how it can effectively search, by examining the connectivity of the phenotypic landscape it is hoped to understand this. It is concluded that the addition of an evolvable Derivation Tree expansion order makes the phenotypic landscape associated with πGE very densely connected, with solutions now linked via a single mutation event that were not previously connected.
Michael O'neill - One of the best experts on this subject based on the ideXlab platform.
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EuroGP - Grammar Design for Derivation Tree Based Genetic Programming Systems
Lecture Notes in Computer Science, 2016Co-Authors: Stefan Forstenlechner, Miguel Nicolau, David Fagan, Michael O'neillAbstract:Grammar-based genetic programming systems have gained interest in recent decades and are widely used nowadays. Although researchers normally present the grammar used to solve a certain problem, they seldom write about processes used to construct the grammar. This paper sheds some light on how to design a grammar that not only covers the search space, but also supports the search process in finding good solutions. The focus lies on context free grammar guided systems using Derivation Tree crossover and mutation, in contrast to linearised grammar based systems. Several grammars are presented encompassing the search space of sorting networks and show concepts which apply to general grammar design. An analysis of the search operators on different grammar is undertaken and performance examined on the sorting network problem. The results show that the overall structure for Derivation Trees created by the grammar has little effect on the performance, but still affects the genetic material changed by search operators.
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EuroGP - Understanding expansion order and phenotypic connectivity in πGE
Lecture Notes in Computer Science, 2013Co-Authors: David Fagan, Michael O'neill, Erik Hemberg, Seán McgarraghyAbstract:Since its inception, πGE has used evolution to guide the order of how to construct Derivation Trees. It was hypothesised that this would allow evolution to adjust the order of expansion during the run and thus help with search. This research aims to identify if a specific order is reachable, how reachable it may be, and goes on to investigate what happens to the expansion order during a πGE run. It is concluded that within πGE we do not evolve towards a specific order but a rather distribution of orders. The added complexity that an evolvable order gives πGE can make it difficult to understand how it can effectively search, by examining the connectivity of the phenotypic landscape it is hoped to understand this. It is concluded that the addition of an evolvable Derivation Tree expansion order makes the phenotypic landscape associated with πGE very densely connected, with solutions now linked via a single mutation event that were not previously connected.
