LARCA - Laboratori d'Algorísmia Relacional, Complexitat i Aprenentatge
http://hdl.handle.net/2117/3486
2017-12-14T22:57:19ZMethods of class field theory to separate logics over finite residue classes and circuit complexity
http://hdl.handle.net/2117/111902
Methods of class field theory to separate logics over finite residue classes and circuit complexity
Arratia Quesada, Argimiro Alejandro; Ortiz, Carlos E.
Separations among the first-order logic Res(0,+,×) of finite residue classes, its extensions with generalized quantifiers, and in the presence of a built-in order are shown in this article, using algebraic methods from class field theory. These methods include classification of spectra of sentences over finite residue classes as systems of congruences, and the study of their h-densities over the set of all prime numbers, for various functions h on the natural numbers. Over ordered structures, the logic of finite residue classes and extensions are known to capture DLOGTIME-uniform circuit complexity classes ranging from AC to TC. Separating these circuit complexity classes is directly related to classifying the h-density of spectra of sentences in the corresponding logics of finite residue classes. General conditions are further shown in this work for a logic over the finite residue classes to have a sentence whose spectrum has no h-density. A corollary of this characterization of spectra of sentences is that in Res(0,+,×,<)+M, the logic of finite residue classes with built-in order and extended with the majority quantifier M, there are sentences whose spectrum have no exponential density.
This is a pre-copyedited, author-produced version of an article accepted for publication in Journal of logic and computation following peer review.
2017-12-13T13:37:18ZArratia Quesada, Argimiro AlejandroOrtiz, Carlos E.Separations among the first-order logic Res(0,+,×) of finite residue classes, its extensions with generalized quantifiers, and in the presence of a built-in order are shown in this article, using algebraic methods from class field theory. These methods include classification of spectra of sentences over finite residue classes as systems of congruences, and the study of their h-densities over the set of all prime numbers, for various functions h on the natural numbers. Over ordered structures, the logic of finite residue classes and extensions are known to capture DLOGTIME-uniform circuit complexity classes ranging from AC to TC. Separating these circuit complexity classes is directly related to classifying the h-density of spectra of sentences in the corresponding logics of finite residue classes. General conditions are further shown in this work for a logic over the finite residue classes to have a sentence whose spectrum has no h-density. A corollary of this characterization of spectra of sentences is that in Res(0,+,×,<)+M, the logic of finite residue classes with built-in order and extended with the majority quantifier M, there are sentences whose spectrum have no exponential density.Examples of CF-bi-inmune and CF-levelable sets in LOGSPACE
http://hdl.handle.net/2117/110922
Examples of CF-bi-inmune and CF-levelable sets in LOGSPACE
Balcázar Navarro, José Luis; Díaz Cort, Josep; Gabarró Vallès, Joaquim
We find sets in the class LOGSPACE (on-line) that do not have good respectively approximations by context-free languages. For that we introduce the languages CF-bi-inmune and CF-levelable. We prove the results by defining directectly the sets and obtaining the properties via pumping arguments.; Trobem conjunts en la classe LOGSPACE (on-line) que no tenen bones respectivament òptimes aproximacions per llenguatges incontextuals. Per això introduïm els llenguatges CF-bi-inmune i CF-nivellable. Demostrem els resultats directament, definim els llenguatges i demostrem les propietats mitjançant el lema d'iteracció
2017-11-20T14:52:27ZBalcázar Navarro, José LuisDíaz Cort, JosepGabarró Vallès, JoaquimWe find sets in the class LOGSPACE (on-line) that do not have good respectively approximations by context-free languages. For that we introduce the languages CF-bi-inmune and CF-levelable. We prove the results by defining directectly the sets and obtaining the properties via pumping arguments.
Trobem conjunts en la classe LOGSPACE (on-line) que no tenen bones respectivament òptimes aproximacions per llenguatges incontextuals. Per això introduïm els llenguatges CF-bi-inmune i CF-nivellable. Demostrem els resultats directament, definim els llenguatges i demostrem les propietats mitjançant el lema d'iteraccióConnections among non uniform models for problems requiring high amount of resources
http://hdl.handle.net/2117/110914
Connections among non uniform models for problems requiring high amount of resources
Balcázar Navarro, José Luis; Gabarró Vallès, Joaquim
We characterize in terms of oracle Turing machines the classes defined by exponential lower bounds on some nonuniform complexity measures. After, we use the same methods to give a new characterization of classes defined by polynomial and polylog upper bounds, obtaining an unified approach to deal with upper and lower bounds. The measures are the initial index, the context-free cost, and the boolean circuits size. We interpret oir results by discussing a trade-off between oracle information and compued information for oracle Turing machines.; Caracteritzem per màquines de Turing amb oracles, classes de complexitat definides per fites interiors exponencials sobre mesures no uniformes. Els mateixos mètodes ens permeten d'obtenir caracteritzacions de classes definides fer fites superiors polinòmiques i "poly-log", unificant l'estudi de fites superiors amb el de fites inferiors. Les mesures són l'índex inicial, el cost incontextual i el cost booleà. Proposem una interpretació del resultat i discutim l'equilibri entre informació calculada i informació obtinguda de l'oracle.
Preliminary version
2017-11-20T10:32:09ZBalcázar Navarro, José LuisGabarró Vallès, JoaquimWe characterize in terms of oracle Turing machines the classes defined by exponential lower bounds on some nonuniform complexity measures. After, we use the same methods to give a new characterization of classes defined by polynomial and polylog upper bounds, obtaining an unified approach to deal with upper and lower bounds. The measures are the initial index, the context-free cost, and the boolean circuits size. We interpret oir results by discussing a trade-off between oracle information and compued information for oracle Turing machines.
Caracteritzem per màquines de Turing amb oracles, classes de complexitat definides per fites interiors exponencials sobre mesures no uniformes. Els mateixos mètodes ens permeten d'obtenir caracteritzacions de classes definides fer fites superiors polinòmiques i "poly-log", unificant l'estudi de fites superiors amb el de fites inferiors. Les mesures són l'índex inicial, el cost incontextual i el cost booleà. Proposem una interpretació del resultat i discutim l'equilibri entre informació calculada i informació obtinguda de l'oracle.Manual de POSTOFF : nueva versión
http://hdl.handle.net/2117/110902
Manual de POSTOFF : nueva versión
Balcázar Navarro, José Luis
Un programa adaptador de textos para que el formateador DSR Runoff se haga amiguete de la impresora LA100. Documentación correspondiente a la versión 3.0. Creado por José Luis Balcázar en la F.I.B. durante 1984.
Sustituye edición RT 85/02
2017-11-20T08:55:01ZBalcázar Navarro, José LuisUn programa adaptador de textos para que el formateador DSR Runoff se haga amiguete de la impresora LA100. Documentación correspondiente a la versión 3.0. Creado por José Luis Balcázar en la F.I.B. durante 1984.On some "non uniform" complexity measures
http://hdl.handle.net/2117/110729
On some "non uniform" complexity measures
Balcázar Navarro, José Luis; Díaz Cort, Josep; Gabarró Vallès, Joaquim
Non-uniform complexity measures origined in Automata and Formal Languages Theory are characterized in terms of well-known uniform complexity classes. The initial index of languages is introduced by means of several computational models. It is shown to be closely related to context-free cost, boolean circuits straight line programs, and Turing machines with sparse oracles and time or space bounds.
2017-11-16T09:17:25ZBalcázar Navarro, José LuisDíaz Cort, JosepGabarró Vallès, JoaquimNon-uniform complexity measures origined in Automata and Formal Languages Theory are characterized in terms of well-known uniform complexity classes. The initial index of languages is introduced by means of several computational models. It is shown to be closely related to context-free cost, boolean circuits straight line programs, and Turing machines with sparse oracles and time or space bounds.Diameter minimization in networks for SIMD machines
http://hdl.handle.net/2117/110701
Diameter minimization in networks for SIMD machines
Beivide Palacio, Ramon; Balcázar Navarro, José Luis
We propose an algebraic constructive method which allows to find a certain kind of networks having optimal diameter. These interconnection networks have been proposed for SIMD machines. We compare the results with other designs, pointing out the improvement achieved with this method.
2017-11-15T16:07:32ZBeivide Palacio, RamonBalcázar Navarro, José LuisWe propose an algebraic constructive method which allows to find a certain kind of networks having optimal diameter. These interconnection networks have been proposed for SIMD machines. We compare the results with other designs, pointing out the improvement achieved with this method.Uniform characterizations of non-uniform complexity measures
http://hdl.handle.net/2117/110675
Uniform characterizations of non-uniform complexity measures
Balcázar Navarro, José Luis; Díaz Cort, Josep; Gabarró Vallès, Joaquim
The class PSPACE/ply of sets decided within polynomial space by machines with polynomial advices is characterized in several way: we give an algebraic characterization, a parallel model characterization. Finally we define a dual class and state some of its properties.
2017-11-15T12:09:44ZBalcázar Navarro, José LuisDíaz Cort, JosepGabarró Vallès, JoaquimThe class PSPACE/ply of sets decided within polynomial space by machines with polynomial advices is characterized in several way: we give an algebraic characterization, a parallel model characterization. Finally we define a dual class and state some of its properties.Deriving specifications of embeddings in recursive program design
http://hdl.handle.net/2117/110673
Deriving specifications of embeddings in recursive program design
Roselló Balanyà, Celestí; Balcázar Navarro, José Luis; Peña Marí, Ricardo
The design of recursive functions is a well-studied subject. Design methods require a specification to start with, however, when an embedding design is attempted at, it is not clear how the specification of the embedding relates to that of the initial function. We propose a method for deriving specifications of embeddings. We show how other known formal methods, such as loop derivation or program transformation, can be related to our method in a clear fashion. The use of embedding to enhance the efficiency of programs is also discussed.
2017-11-15T11:55:04ZRoselló Balanyà, CelestíBalcázar Navarro, José LuisPeña Marí, RicardoThe design of recursive functions is a well-studied subject. Design methods require a specification to start with, however, when an embedding design is attempted at, it is not clear how the specification of the embedding relates to that of the initial function. We propose a method for deriving specifications of embeddings. We show how other known formal methods, such as loop derivation or program transformation, can be related to our method in a clear fashion. The use of embedding to enhance the efficiency of programs is also discussed.Characterization of the CPAP-treated patient population in Catalonia
http://hdl.handle.net/2117/109111
Characterization of the CPAP-treated patient population in Catalonia
Turino, Cecilia; Bertrán, Sandra; Gavaldà Mestre, Ricard; Teixidó, Ivan; Woehrle, Holger; Rué, Montserrat; Solsona, Francesc; Escarrabill, Joan; Colls, Cristina; García Altés, Anna; Batlle, Jordi de; Sánchez de la Torre, Manuel; Barbé, Ferran
There are different phenotypes of obstructive sleep apnoea (OSA), many of which have not been characterised. Identification of these different phenotypes is important in defining prognosis and guiding the therapeutic strategy. The aim of this study was to characterise the entire population of continuous positive airway pressure (CPAP)-treated patients in Catalonia and identify specific patient profiles using cluster analysis. A total of 72,217 CPAP-treated patients who contacted the Catalan Health System (Cat-Salut) during the years 2012 and 2013 were included. Six clusters were identified, classified as “Neoplastic patients” (Cluster 1, 10.4%), “Metabolic syndrome patients” (Cluster 2, 27.7%), “Asthmatic patients” (Cluster 3, 5.8%), “Musculoskeletal and joint disorder patients” (Cluster 4, 10.3%), “Patients with few comorbidities” (Cluster 5, 35.6%) and “Oldest and cardiac disease patients” (Cluster 6, 10.2%). Healthcare facility use and mortality were highest in patients from Cluster 1 and 6. Conversely, patients in Clusters 2 and 4 had low morbidity, mortality and healthcare resource use. Our findings highlight the heterogeneity of CPAP-treated patients, and suggest that OSA is associated with a different prognosis in the clusters identified. These results suggest the need for a comprehensive and individualised approach to CPAP treatment of OSA.
2017-10-25T08:17:33ZTurino, CeciliaBertrán, SandraGavaldà Mestre, RicardTeixidó, IvanWoehrle, HolgerRué, MontserratSolsona, FrancescEscarrabill, JoanColls, CristinaGarcía Altés, AnnaBatlle, Jordi deSánchez de la Torre, ManuelBarbé, FerranThere are different phenotypes of obstructive sleep apnoea (OSA), many of which have not been characterised. Identification of these different phenotypes is important in defining prognosis and guiding the therapeutic strategy. The aim of this study was to characterise the entire population of continuous positive airway pressure (CPAP)-treated patients in Catalonia and identify specific patient profiles using cluster analysis. A total of 72,217 CPAP-treated patients who contacted the Catalan Health System (Cat-Salut) during the years 2012 and 2013 were included. Six clusters were identified, classified as “Neoplastic patients” (Cluster 1, 10.4%), “Metabolic syndrome patients” (Cluster 2, 27.7%), “Asthmatic patients” (Cluster 3, 5.8%), “Musculoskeletal and joint disorder patients” (Cluster 4, 10.3%), “Patients with few comorbidities” (Cluster 5, 35.6%) and “Oldest and cardiac disease patients” (Cluster 6, 10.2%). Healthcare facility use and mortality were highest in patients from Cluster 1 and 6. Conversely, patients in Clusters 2 and 4 had low morbidity, mortality and healthcare resource use. Our findings highlight the heterogeneity of CPAP-treated patients, and suggest that OSA is associated with a different prognosis in the clusters identified. These results suggest the need for a comprehensive and individualised approach to CPAP treatment of OSA.Optimal distance networks of low degree for parallel computers
http://hdl.handle.net/2117/108974
Optimal distance networks of low degree for parallel computers
Beivide Palacio, Ramon; Herrada Lillo, Enrique; Balcázar Navarro, José Luis; Arruabarrena, Agustín
We introduce and study a family of interconnection schemes, the Midimew networks, based on circulant graphs of degree 4. A family of such circulants is determined and shown to be optimal with respect to two distance parameters simultaneously, namely maximum distance and average distance, among all circulants of degree 4.. These graphs are regular, point-symmetric, and maximally connected, and one such optimal graph exists for any given number of nodes. The proposed interconnection schemes consist of mesh-connected networks with wrap-around links, and are isomorphic to the optimal distance circulants previously considered. Ways to construct one such network for any number of nodes are shown, their good properties to build interconnection schemes for multicomputers are examined, and some interesting particular cases are discussed. The problem of routing is also addressed, and a basic algorithm is provided which is adequate for implementing the routing policy required to convey messages, traversing shortest paths between nodes.
2017-10-23T13:37:52ZBeivide Palacio, RamonHerrada Lillo, EnriqueBalcázar Navarro, José LuisArruabarrena, AgustínWe introduce and study a family of interconnection schemes, the Midimew networks, based on circulant graphs of degree 4. A family of such circulants is determined and shown to be optimal with respect to two distance parameters simultaneously, namely maximum distance and average distance, among all circulants of degree 4.. These graphs are regular, point-symmetric, and maximally connected, and one such optimal graph exists for any given number of nodes. The proposed interconnection schemes consist of mesh-connected networks with wrap-around links, and are isomorphic to the optimal distance circulants previously considered. Ways to construct one such network for any number of nodes are shown, their good properties to build interconnection schemes for multicomputers are examined, and some interesting particular cases are discussed. The problem of routing is also addressed, and a basic algorithm is provided which is adequate for implementing the routing policy required to convey messages, traversing shortest paths between nodes.