Articles de revista
http://hdl.handle.net/2117/3517
2017-03-26T01:54:35ZQuasipolynomial size frege proofs of Frankl's Theorem on the trace of sets
http://hdl.handle.net/2117/100899
Quasipolynomial size frege proofs of Frankl's Theorem on the trace of sets
Aisenberg, James; Bonet Carbonell, M. Luisa; Buss, Sam
We extend results of Bonet, Buss and Pitassi on Bondy's Theorem and of Nozaki, Arai and Arai on Bollobas' Theorem by proving that Frankl's Theorem on the trace of sets has quasipolynomial size Frege proofs. For constant values of the parameter t, we prove that Frankl's Theorem has polynomial size AC(0)-Frege proofs from instances of the pigeonhole principle.
2017-02-13T11:15:11ZAisenberg, JamesBonet Carbonell, M. LuisaBuss, SamWe extend results of Bonet, Buss and Pitassi on Bondy's Theorem and of Nozaki, Arai and Arai on Bollobas' Theorem by proving that Frankl's Theorem on the trace of sets has quasipolynomial size Frege proofs. For constant values of the parameter t, we prove that Frankl's Theorem has polynomial size AC(0)-Frege proofs from instances of the pigeonhole principle.The scaling of the minimum sum of edge lengths in uniformly random trees
http://hdl.handle.net/2117/88535
The scaling of the minimum sum of edge lengths in uniformly random trees
Esteban Ángeles, Juan Luis; Ferrer Cancho, Ramon; Gómez Rodríguez, Carlos
The minimum linear arrangement problem on a network consists of finding the minimum sum of edge lengths that can be achieved when the vertices are arranged linearly. Although there are algorithms to solve this problem on trees in polynomial time, they have remained theoretical and have not been implemented in practical contexts to our knowledge. Here we use one of those algorithms to investigate the growth of this sum as a function of the size of the tree in uniformly random trees. We show that this sum is bounded above by its value in a star tree. We also show that the mean edge length grows logarithmically in optimal linear arrangements, in stark contrast to the linear growth that is expected on optimal arrangements of star trees or on random linear arrangements.
2016-07-06T09:32:34ZEsteban Ángeles, Juan LuisFerrer Cancho, RamonGómez Rodríguez, CarlosThe minimum linear arrangement problem on a network consists of finding the minimum sum of edge lengths that can be achieved when the vertices are arranged linearly. Although there are algorithms to solve this problem on trees in polynomial time, they have remained theoretical and have not been implemented in practical contexts to our knowledge. Here we use one of those algorithms to investigate the growth of this sum as a function of the size of the tree in uniformly random trees. We show that this sum is bounded above by its value in a star tree. We also show that the mean edge length grows logarithmically in optimal linear arrangements, in stark contrast to the linear growth that is expected on optimal arrangements of star trees or on random linear arrangements.The computability path ordering
http://hdl.handle.net/2117/85100
The computability path ordering
Blanqui, Frédéric; Jouannaud, Jean Pierre; Rubio Gimeno, Alberto
This paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by lifting a precedence on function symbols. A first version, core CPO, is essentially obtained from the higher-order recursive path ordering (HORPO) by eliminating type checks from some recursive calls and by incorporating the treatment of bound variables as in the com-putability closure. The well-foundedness proof shows that core CPO captures the essence of computability arguments ^#224, la Tait and Girard, therefore explaining its name. We further show that no further type check can be eliminated from its recursive calls without loosing well-foundedness, but for one for which we found no counterexample yet. Two extensions of core CPO are then introduced which allow one to consider: the first, higher-order inductive types; the second, a precedence in which some function symbols are smaller than application and abstraction.
2016-04-04T09:50:47ZBlanqui, FrédéricJouannaud, Jean PierreRubio Gimeno, AlbertoThis paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by lifting a precedence on function symbols. A first version, core CPO, is essentially obtained from the higher-order recursive path ordering (HORPO) by eliminating type checks from some recursive calls and by incorporating the treatment of bound variables as in the com-putability closure. The well-foundedness proof shows that core CPO captures the essence of computability arguments ^#224, la Tait and Girard, therefore explaining its name. We further show that no further type check can be eliminated from its recursive calls without loosing well-foundedness, but for one for which we found no counterexample yet. Two extensions of core CPO are then introduced which allow one to consider: the first, higher-order inductive types; the second, a precedence in which some function symbols are smaller than application and abstraction.Normal higher-order termination
http://hdl.handle.net/2117/79284
Normal higher-order termination
Jouannaud, Jean Pierre; Rubio Gimeno, Alberto
We extend the termination proof methods based on reduction orderings to higher-order rewriting systems based on higher-order pattern matching. We accommodate, on the one hand, a weakly polymorphic, algebraic extension of Church's simply typed λ-calculus and, on the other hand, any use of eta, as a reduction, as an expansion, or as an equation. The user's rules may be of any type in this type system, either a base, functional, or weakly polymorphic type.
2015-11-16T09:58:07ZJouannaud, Jean PierreRubio Gimeno, AlbertoWe extend the termination proof methods based on reduction orderings to higher-order rewriting systems based on higher-order pattern matching. We accommodate, on the one hand, a weakly polymorphic, algebraic extension of Church's simply typed λ-calculus and, on the other hand, any use of eta, as a reduction, as an expansion, or as an equation. The user's rules may be of any type in this type system, either a base, functional, or weakly polymorphic type.Efficiently calculating evolutionary tree measures using SAT
http://hdl.handle.net/2117/12674
Efficiently calculating evolutionary tree measures using SAT
Bonet Carbonell, M. Luisa; John, Katherine St.
We develop techniques to calculate important measures in evolutionary biology by encoding to CNF formulas and using powerful SAT solvers. Comparing evolutionary trees is a necessary step in tree reconstruction algorithms, locating recombination and lateral gene transfer, and in analyzing and visualizing sets of trees. We focus on two popular comparison measures for trees: the hybridization number and the rooted subtree-prune-and-regraft (rSPR) distance. Both have recently been shown to be NP-hard, and effcient algorithms are needed to compute
and approximate these measures. We encode these as a Boolean formula such that two trees have hybridization number k (or rSPR distance k) if and only if the corresponding formula is satisfiable. We use state-of-the-art SAT solvers to determine if the formula encoding the measure has a satisfying assignment. Our encoding also provides a rich
source of real-world SAT instances, and we include a comparison of several recent solvers (minisat, adaptg2wsat, novelty+p, Walksat, March KS and SATzilla).
2011-05-30T14:45:23ZBonet Carbonell, M. LuisaJohn, Katherine St.We develop techniques to calculate important measures in evolutionary biology by encoding to CNF formulas and using powerful SAT solvers. Comparing evolutionary trees is a necessary step in tree reconstruction algorithms, locating recombination and lateral gene transfer, and in analyzing and visualizing sets of trees. We focus on two popular comparison measures for trees: the hybridization number and the rooted subtree-prune-and-regraft (rSPR) distance. Both have recently been shown to be NP-hard, and effcient algorithms are needed to compute
and approximate these measures. We encode these as a Boolean formula such that two trees have hybridization number k (or rSPR distance k) if and only if the corresponding formula is satisfiable. We use state-of-the-art SAT solvers to determine if the formula encoding the measure has a satisfying assignment. Our encoding also provides a rich
source of real-world SAT instances, and we include a comparison of several recent solvers (minisat, adaptg2wsat, novelty+p, Walksat, March KS and SATzilla).Mining frequent closed rooted trees
http://hdl.handle.net/2117/6835
Mining frequent closed rooted trees
Balcázar Navarro, José Luis; Bifet Figuerol, Albert Carles; Lozano Bojados, Antoni
Many knowledge representation mechanisms are based on tree-like structures, thus symbolizing the fact that certain pieces of information are related in one sense or another. There exists a well-studied process of closure-based data mining in the itemset framework: we consider the extension of this process into trees. We focus mostly on the case where labels on the nodes are nonexistent or unreliable, and discuss algorithms for closurebased mining that only rely on the root of the tree and the link structure.
We provide a notion of intersection that leads to a deeper understanding of the notion of support-based closure, in terms of an actual closure operator.
We describe combinatorial characterizations and some properties of ordered trees, discuss their applicability to unordered trees, and rely on them to design efficient algorithms for mining frequent closed subtrees both in the ordered and the unordered settings. Empirical validations and comparisons with alternative algorithms are provided.
2010-03-30T09:00:52ZBalcázar Navarro, José LuisBifet Figuerol, Albert CarlesLozano Bojados, AntoniMany knowledge representation mechanisms are based on tree-like structures, thus symbolizing the fact that certain pieces of information are related in one sense or another. There exists a well-studied process of closure-based data mining in the itemset framework: we consider the extension of this process into trees. We focus mostly on the case where labels on the nodes are nonexistent or unreliable, and discuss algorithms for closurebased mining that only rely on the root of the tree and the link structure.
We provide a notion of intersection that leads to a deeper understanding of the notion of support-based closure, in terms of an actual closure operator.
We describe combinatorial characterizations and some properties of ordered trees, discuss their applicability to unordered trees, and rely on them to design efficient algorithms for mining frequent closed subtrees both in the ordered and the unordered settings. Empirical validations and comparisons with alternative algorithms are provided.