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Toniann Pitassi - One of the best experts on this subject based on the ideXlab platform.

  • exponential time space speedups for resolution and the pspace completeness of black white pebbling
    Foundations of Computer Science, 2007
    Co-Authors: P Herte, Toniann Pitassi
    Abstract:

    The complexity of the Black-White Pebbling Game has remained open for 30 years. It was devised to capture the power of non-deterministic space bounded computation. Since then it has been applied to problems in diverse areas of computer science including VLSI design and more recently propositional proof complexity. In this paper we show that the Black-While Pebbling Game is PSPACE-complete. We then use similar ideas in a more complicated reduction to prove the PSPACE-completeness of Resolution space. The reduction also yields a surprising exponential time/space speedup for Resolution in which an increase of 3 units of space results in an exponential decrease in proof-size.

  • an exponential time space speedup for resolution
    Electronic Colloquium on Computational Complexity, 2007
    Co-Authors: Philipp Hertel, Toniann Pitassi
    Abstract:

    Satisfiability algorithms have become one of the most practi cal and successful approaches for solving a variety of real-world problems, including hardware verifi cation, experimental design, planning and diagnosis problems. The main reason for the success is due to highly optimized algorithms for SAT based on resolution. The most successful of these is clause learning, a DPLL scheme based on caching intermediate clauses that are “learned” throughout the backtrack search procedure. The main bottleneck to this approach is space, and thus there has been a tremendous amount of research aimed at identifying good heuristics for deciding what information to cache. Haken first suggested a formal approach to this issue, and Ben-Sasson [3] posed the question of whether there is a time/space tradeoff for resolution. Our main result is an optimal time/space tradeoff for resolution. Namely, we present an infinite family of propositional formulas whose minimal space proofs all have exponential time, but if just three extra units of storage are allowed, then the formulas can be proved in linear time. We also prove another related theorem. Given an unsatisfiabl e formula F and an integer k, the resolution space problem is to determine if F has a resolution proof which can be verified using space k. We prove that this problem is PSPACE complete.

P Herte - One of the best experts on this subject based on the ideXlab platform.

  • exponential time space speedups for resolution and the pspace completeness of black white pebbling
    Foundations of Computer Science, 2007
    Co-Authors: P Herte, Toniann Pitassi
    Abstract:

    The complexity of the Black-White Pebbling Game has remained open for 30 years. It was devised to capture the power of non-deterministic space bounded computation. Since then it has been applied to problems in diverse areas of computer science including VLSI design and more recently propositional proof complexity. In this paper we show that the Black-While Pebbling Game is PSPACE-complete. We then use similar ideas in a more complicated reduction to prove the PSPACE-completeness of Resolution space. The reduction also yields a surprising exponential time/space speedup for Resolution in which an increase of 3 units of space results in an exponential decrease in proof-size.

Th Schlumprecht - One of the best experts on this subject based on the ideXlab platform.

Ekrem Savas - One of the best experts on this subject based on the ideXlab platform.

Abdillah, Said Amana - One of the best experts on this subject based on the ideXlab platform.

  • Extensions au cadre Banachique de la notion d'opérateur de Hilbert-Schmidt
    2020
    Co-Authors: Abdillah, Said Amana
    Abstract:

    Cette thèse est consacrée à l’extension au cadre Banachique de la notion d’opérateur de Hilbert-Schmidt. Dans un premier temps, on étudie d’une part les opérateurs p-sommants dans un espace de Banach X vers un autre espace de Banach Y et d’autre part, les opérateurs gamma-radonifiants dans un espace de Hilbert vers un autre espace de Banach.Dans un second temps, on s'intéresse aux opérateurs gamma-sommants dans des espaces de Banach, qui coïncident avec les opérateurs de Rademacher-bornés, ce qui nous amène aux opérateurs presque sommants. Enfin, on en déduit plusieurs généralisations naturelles de la notion d’opérateur de Hilbert-Schmidt aux espaces de Banach.-Les classes des opérateurs p-sommants de X dans Y .-La classe des opérateurs presque sommants de X dans Y qui coïncide avec la classe des opérateurs gamma-radonifiants de X dans Y.-La classe des opérateurs faible* 1-nucléaires de X dans Y.This thesis is devoted to extending the notion of Banach Hilbert-Schmidt operator to the framework of Banach spaces. In a first step, we study p-summing operators from a Banach space X into a Banach space Y and gamma-radoniyfing operators from a Hilbert space into a Banach space. In a second step, we discuss gamma-summing operators between Banach spaces, which coincide with Rademacher-bounded operators, which leads to the notion of almost summing operators. Finally, we present serval natural generalizations of the notion of Hilbert-Schmidt operator to Banach spaces.- Classes of p-summing operators from X into Y. - The class of almost summing operators from X into Y, which coincides with the class of gamma-radoniyfing operators from X into Y.- The class of weak*1-nuclear operators from X into Y

  • Extensions au cadre Banachique de la notion d'opérateur de Hilbert-Schmidt
    2012
    Co-Authors: Abdillah, Said Amana, Esterle Jean, Haak, Bernhard Hermann
    Abstract:

    Cette thèse est consacrée à l extension au cadre Banachique de la notion d opérateur de Hilbert-Schmidt. Dans un premier temps, on étudie d une part les opérateurs p-sommants dans un espace de Banach X vers un autre espace de Banach Y et d autre part, les opérateurs gamma-radonifiants dans un espace de Hilbert vers un autre espace de Banach.Dans un second temps, on s'intéresse aux opérateurs gamma-sommants dans des espaces de Banach, qui coïncident avec les opérateurs de Rademacher-bornés, ce qui nous amène aux opérateurs presque sommants. Enfin, on en déduit plusieurs généralisations naturelles de la notion d opérateur de Hilbert-Schmidt aux espaces de Banach.-Les classes des opérateurs p-sommants de X dans Y .-La classe des opérateurs presque sommants de X dans Y qui coïncide avec la classe des opérateurs gamma-radonifiants de X dans Y.-La classe des opérateurs faible* 1-nucléaires de X dans Y.This thesis is devoted to extending the notion of Banach Hilbert-Schmidt operator to the framework of Banach spaces. In a first step, we study p-summing operators from a Banach space X into a Banach space Y and gamma-radoniyfing operators from a Hilbert space into a Banach space. In a second step, we discuss gamma-summing operators between Banach spaces, which coincide with Rademacher-bounded operators, which leads to the notion of almost summing operators. Finally, we present serval natural generalizations of the notion of Hilbert-Schmidt operator to Banach spaces.- Classes of p-summing operators from X into Y. - The class of almost summing operators from X into Y, which coincides with the class of gamma-radoniyfing operators from X into Y.- The class of weak*1-nuclear operators from X into Y.BORDEAUX1-Bib.electronique (335229901) / SudocSudocFranceF