scholarly journals Small Circuits and Dual Weak PHP in the Universal Theory of p-time Algorithms

2021 ◽  
Vol 22 (2) ◽  
pp. 1-4
Author(s):  
Jan Krajíček
Keyword(s):  
Computational Complexity ◽  
Time Function ◽  
Truth Table ◽  
Universal Theory ◽  
Pigeonhole Principle ◽  
Polynomial Size ◽  
Complexity Hypothesis

We prove, under a computational complexity hypothesis, that it is consistent with the true universal theory of p-time algorithms that a specific p-time function extending bits to bits violates the dual weak pigeonhole principle: Every string equals the value of the function for some . The function is the truth-table function assigning to a circuit the table of the function it computes and the hypothesis is that every language in P has circuits of a fixed polynomial size .

L’acquisition des clitiques nominatifs et des clitiques objets en français

2000 ◽  
Vol 45 (1-2) ◽  
pp. 119-157 ◽  
Author(s):  
Celia Jakubowicz ◽  
Catherine Rigaut
Keyword(s):  
Computational Complexity ◽  
Production Task ◽  
Spontaneous Interaction ◽  
Object Clitics ◽  
French Speaking ◽  
Third Person ◽  
Complexity Hypothesis ◽  
Better Than

AbstractThis article presents and discusses data on nominative and object clitics used by twelve monolingual French-speaking children aged 2;0 to 2;7 years in a spontaneous interaction setting and in an elicited production task. It is shown that nominative clitics surpass object clitics, and that reflexive clitics fare better than accusative clitics. It is argued that these two dissociations are compatible with the computational complexity hypothesis put forth by Jakubowicz and Nash (to appear), applied to the analysis of third person Romance pronominal clitics proposed by Jakubowicz, Nash, Rigaut, and Gérard (1998).

scholarly journals ON THE PROOF COMPLEXITY OF THE NISAN–WIGDERSON GENERATOR BASED ON A HARD NP ∩ coNP FUNCTION

2011 ◽  
Vol 11 (01) ◽  
pp. 11-27 ◽  
Author(s):  
JAN KRAJÍČEK
Keyword(s):  
Propositional Logic ◽  
Reflection Principle ◽  
Proof Complexity ◽  
Proof System ◽  
Universal Theory ◽  
General Statement ◽  
Disjunction Property ◽  
Proof Systems ◽  
Polynomial Size ◽  
Theory Formula

Let g be a map defined as the Nisan–Wigderson generator but based on an NP ∩ coNP -function f. Any string b outside the range of g determines a propositional tautology τ(g)b expressing this fact. Razborov [27] has conjectured that if f is hard on average for P/poly then these tautologies have no polynomial size proofs in the Extended Frege system EF. We consider a more general Statement (S) that the tautologies have no polynomial size proofs in any propositional proof system. This is equivalent to the statement that the complement of the range of g contains no infinite NP set. We prove that Statement (S) is consistent with Cook' s theory PV and, in fact, with the true universal theory T PV in the language of PV. If PV in this consistency statement could be extended to "a bit" stronger theory (properly included in Buss's theory [Formula: see text]) then Razborov's conjecture would follow, and if TPV could be added too then Statement (S) would follow. We discuss this problem in some detail, pointing out a certain form of reflection principle for propositional logic, and we introduce a related feasible disjunction property of proof systems.

scholarly journals QUASIPOLYNOMIAL SIZE FREGE PROOFS OF FRANKL’S THEOREM ON THE TRACE OF SETS

2016 ◽  
Vol 81 (2) ◽  
pp. 687-710 ◽  
Author(s):  
JAMES AISENBERG ◽  
MARIA LUISA BONET ◽  
SAM BUSS
Keyword(s):  
Pigeonhole Principle ◽  
Polynomial Size

AbstractWe extend results of Bonet, Buss and Pitassi on Bondy’s Theorem and of Nozaki, Arai and Arai on Bollobás’ Theorem by proving that Frankl’s Theorem on the trace of sets has quasipolynomial size Frege proofs. For constant values of the parametert, we prove that Frankl’s Theorem has polynomial size AC0-Frege proofs from instances of the pigeonhole principle.

scholarly journals Polynomial size proofs of the propositional pigeonhole principle

1987 ◽  
Vol 52 (4) ◽  
pp. 916-927 ◽  
Author(s):  
Samuel R. Buss
Keyword(s):  
Bounded Arithmetic ◽  
Pigeonhole Principle ◽  
Polynomial Size ◽  
Frege Systems

AbstractCook and Reckhow defined a propositional formulation of the pigeonhole principle. This paper shows that there are Frege proofs of this propositional pigeonhole principle of polynomial size. This together with a result of Haken gives another proof of Urquhart's theorem that Frege systems have an exponential speedup over resolution. We also discuss connections to provability in theories of bounded arithmetic.

Bipolar Abstract Argumentation with Dual Attacks and Supports

2020 ◽  
Author(s):  
Nico Potyka
Keyword(s):  
Computational Complexity ◽  
Decision Problems ◽  
Abstract Argumentation ◽  
Stable Semantics ◽  
Support Relations ◽  
Support Relationships ◽  
Computational Properties ◽  
Inherent Tendency

Bipolar abstract argumentation frameworks allow modeling decision problems by defining pro and contra arguments and their relationships. In some popular bipolar frameworks, there is an inherent tendency to favor either attack or support relationships. However, for some applications, it seems sensible to treat attack and support equally. Roughly speaking, turning an attack edge into a support edge, should just invert its meaning. We look at a recently introduced bipolar argumentation semantics and two novel alternatives and discuss their semantical and computational properties. Interestingly, the two novel semantics correspond to stable semantics if no support relations are present and maintain the computational complexity of stable semantics in general bipolar frameworks.

Synergetic Theory of Document in Evolution of Document Science

2018 ◽  
pp. 1060-1068
Author(s):  
Galina A. Dvoenosova ◽  
Keyword(s):  
Social Role ◽  
Scientific Study ◽  
Self Organization ◽  
Universal Theory ◽  
Social Self ◽  
Social Goal ◽  
The Social ◽  
Synergetic Theory ◽  
First Time

The article assesses synergetic theory of document as a new development in document science. In information society the social role of document grows, as information involves all members of society in the process of documentation. The transformation of document under the influence of modern information technologies increases its interest to representatives of different sciences. Interdisciplinary nature of document as an object of research leads to an ambiguous interpretation of its nature and social role. The article expresses and contends the author's views on this issue. In her opinion, social role of document is incidental to its being a main social tool regulating the life of civilized society. Thus, the study aims to create a scientific theory of document, explaining its nature and social role as a tool of social (goal-oriented) action and social self-organization. Substantiation of this idea is based on application of synergetics (i.e., universal theory of self-organization) to scientific study of document. In the synergetic paradigm, social and historical development is seen as the change of phases of chaos and order, and document is considered a main tool that regulates social relations. Unlike other theories of document, synergetic theory studies document not as a carrier and means of information transfer, but as a unique social phenomenon and universal social tool. For the first time, the study of document steps out of traditional frameworks of office, archive, and library. The document is placed on the scales with society as a global social system with its functional subsystems of politics, economy, culture, and personality. For the first time, the methods of social sciences and modern sociological theories are applied to scientific study of document. This methodology provided a basis for theoretical vindication of nature and social role of document as a tool of social (goal-oriented) action and social self-organization. The study frames a synergetic theory of document with methodological foundations and basic concepts, synergetic model of document, laws of development and effectiveness of document in the social continuum. At the present stage of development of science, it can be considered the highest form of theoretical knowledge of document and its scientific explanatory theory.

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