Now showing items 1-20 of 31

  • A Note on polynomial-size monotone proofs of the pigeon hole principle 

    Atserias, Albert (2000-09)
    External research report
    Open Access
    We see that the version of the pigeon-hole principle in which every hole is forced to receive a pigeon (called onto) and the version in which every pigeon is mapped into exactly one hole (called functional) have ...
  • Automating Resolution is NP-hard 

    Atserias, Albert; Muller, Moritz Martin (Institute of Electrical and Electronics Engineers (IEEE), 2019)
    Conference report
    Open Access
    We show that the problem of finding a Resolution refutation that is at most polynomially longer than a shortest one is NP-hard. In the parlance of proof complexity, Resolution is not automatizable unless P = NP. Indeed, ...
  • Bounded-width QBF is PSPACE-complete 

    Atserias, Albert; Oliva Valls, Sergi (Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2013)
    Conference report
    Open Access
    Tree-width is a well-studied parameter of structures that measures their similarity to a tree. Many important NP-complete problems, such as Boolean satisfiability (SAT), are tractable on bounded tree-width instances. In ...
  • Bounded-width QBF is PSPACE-complete 

    Atserias, Albert; Oliva Valls, Sergi (2014-11-01)
    Article
    Open Access
    Tree-width and path-width are two well-studied parameters of structures that measure their similarity to a tree and a path, respectively. We show that QBF on instances with constant path-width, and hence constant tree-width, ...
  • CALCULABILITAT (Examen 2n quadrim) 

    Atserias, Albert (Universitat Politècnica de Catalunya, 2010-05-31)
    Exam
    Restricted access to the UPC academic community
  • Circular (yet sound) proofs 

    Atserias, Albert; Lauria, Massimo (Springer, 2019)
    Conference report
    Open Access
    We introduce a new way of composing proofs in rule-based proof systems that generalizes tree-like and dag-like proofs. In the new definition, proofs are directed graphs of derived formulas, in which cycles are allowed as ...
  • Clique is hard on average for regular resolution 

    Atserias, Albert; Bonacina, Ilario; Rezende, Susanna F. de; Lauria, Massimo; Nordström, Jakob; Razborov, Alexander (Association for Computing Machinery (ACM), 2018)
    Conference report
    Open Access
    We prove that for k ≪4√n regular resolution requires length nΩ(k) to establish that an Erdős–Rényi graph with appropriately chosen edge density does not contain a k-clique. This lower bound is optimal up to the multiplicative ...
  • Definable ellipsoid method, sums-of-squares proofs, and the isomorphism problem 

    Atserias, Albert; Ochremiak, Joanna (Association for Computing Machinery (ACM), 2018)
    Conference report
    Open Access
    The ellipsoid method is an algorithm that solves the (weak) feasibility and linear optimization problems for convex sets by making oracle calls to their (weak) separation problem. We observe that the previously known method ...
  • Definable inapproximability: new challenges for duplicator 

    Atserias, Albert; Dawar, Anuj (2019)
    Article
    Open Access
    We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P=NP, no polynomial-time algorithm can give an ...
  • Definable inapproximability: New challenges for duplicator 

    Atserias, Albert; Dawar, Anuj (Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018)
    Conference report
    Open Access
    We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an ...
  • Degree lower bounds of tower-type for approximating formulas with parity quantifiers 

    Atserias, Albert; Dawar, Anuj (2014-02-01)
    Article
    Open Access
    Kolaitis and Kopparty have shown that for any first-order formula with parity quantifiers over the language of graphs, there is a family of multivariate polynomials of constant-degree that agree with the formula on all but ...
  • Entailment among probabilistic implications 

    Atserias, Albert; Balcázar Navarro, José Luis (Institute of Electrical and Electronics Engineers (IEEE), 2015)
    Conference report
    Open Access
    We study a natural variant of the implicational fragment of propositional logic. Its formulas are pairs of conjunctions of positive literals, related together by an implicational-like connective, the semantics of this sort ...
  • From unplugged to physically realizable machines, and back 

    Atserias, Albert (2016-03-30)
    Audiovisual
    Restricted access - author's decision
    Around 1936, Alan Turing conceived his model of an automated computer. This was long before the transistor was even discovered. Thus, one would think that Turing's original model could nowadays be considered a piece of ...
  • Generalized satisfiability problems via operator assignments 

    Atserias, Albert; Kolaitis, Phokion; Severini, Simone (2019-09)
    Article
    Open Access
    Schaefer introduced a framework for generalized satisfiability problems on the Boolean domain and characterized the computational complexity of such problems. We investigate an algebraization of Schaefer's framework in ...
  • Lower bounds for DNF-refutations of a relativized weak pigeonhole principle 

    Atserias, Albert; Müller, Moritz; Oliva Valls, Sergi (Institute of Electrical and Electronics Engineers (IEEE), 2013)
    Conference report
    Open Access
    The relativized weak pigeonhole principle states that if at least 2n out of n2 pigeons fly into n holes, then some hole must be doubly occupied. We prove that every DNF-refutation of the CNF encoding of this principle ...
  • Lower bounds for DNF-refutations of a relativized weak pigeonhole principle 

    Atserias, Albert; Müller, Moritz; Oliva Valls, Sergi (2015-06-01)
    Article
    Open Access
    The relativized weak pigeonhole principle states that if at least 2n out of n(2) pigeons fly into n holes, then some hole must be doubly occupied. We prove that every DNF-refutation of the CNF encoding of this principle ...
  • Monotone proofs of the pigeon hole principle 

    Atserias, Albert; Galesi, Nicola; Gavaldà Mestre, Ricard (2000-04)
    External research report
    Open Access
    We study the complexity of proving the Pigeon Hole Principle (PHP) in a monotone variant of the Gentzen Calculus, also known as Geometric Logic. We show that the standard encoding of the PHP as a monotone sequent admits ...
  • Narrow proofs may be maximally long 

    Atserias, Albert; Lauria, Massimo; Nordström, Jakob (2016-07-03)
    Article
    Open Access
    We prove that there are 3-CNF formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size n(Omega(w)). This shows that the simple counting argument that any formula refutable ...
  • Narrow proofs may be maximally long 

    Atserias, Albert; Lauria, Massimo; Nordström, Jakob (Institute of Electrical and Electronics Engineers (IEEE), 2014)
    Conference report
    Open Access
    We prove that there are 3-CNF formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size n¿(w). This shows that the simple counting argument that any formula refutable in ...
  • Non-homogenizable classes of finite structures 

    Atserias, Albert; Torunczyk, Szymon Abram (Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016)
    Conference report
    Open Access
    Homogenization is a powerful way of taming a class of finite structures with several interesting applications in different areas, from Ramsey theory in combinatorics to constraint satisfaction problems (CSPs) in computer ...