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Polynomial Simulation and Refutation of Complex Formulas of Resolution over Linear Equations in Propositional Proof System

Vishwa Nath Maurya, Avadhesh Kumar Maurya
2014 American Journal of Modeling and Optimization  
In this paper, we present that the propositional proof system R(lin) (Resolution over Linear Equations) established by Ran Raz and Iddo Tzameret is not a super system, there exists a sequence of tautologies  ...  , which require proof complexity exponential in size of tautologies.  ...  Since in the late of sixth decade, Tseitin [10] pronounced the first super-polynomial lower bound to the lengths of proofs for resolution; therefore the resolution system is not a super system yet resolution  ... 
doi:10.12691/ajmo-2-1-5 fatcat:qoik3kdlbrbatnjbchzqto2maa

Yet another argument in favour of NP=CoNP [article]

Edward Hermann Haeusler
2020 arXiv   pre-print
The former proof shows how to obtain polynomial and, polynomial in time checkable Dag-like proofs for all purely implicational Minimal logic tautologies.  ...  The existence of repeated parts is a consequence of the redundancy theorem for a family of super-polynomial proofs in the purely implicational Minimal logic.  ...  Thank the proof-theory group at Tuebingen-University, led by prof. Peter Schroeder-Heister. We want to thank Thomas Piecha and M. Arndt.  ... 
arXiv:2101.00003v1 fatcat:p3na5hk4grcevpoesvjx7stli4

The Cook-Reckhow definition [article]

Jan Krajicek
2019 arXiv   pre-print
In this note we shall highlight three particular definitions from the paper: of proof systems, p-simulations and the pigeonhole principle formula, and discuss their role in defining the field.  ...  to the subject as we understand it today, the most significant being Tseitin's 1968 paper, but none of them introduced general notions that would allow to make an explicit and universal link between lengths-of-proofs  ...  The question about the minimum length of a proof of a statement (measured by either the number of steps or by the size, i.e. the number of symbols) was also studied, primarily in the context of speed-up  ... 
arXiv:1909.03691v1 fatcat:yjq26pkixjdujav6kqv6cumtyq

A proper hierarchy of propositional sequent calculi

Noriko H. Arai
1996 Theoretical Computer Science  
In this paper, we show that LK (in tree form) with a cut rule, where the complexity of cut formulas is bounded by (k + 1) has an exponential speed-up over the one bounded by k.  ...  We also show that LK (in tree form) with a bounded complexity cut rule does not polynomially simulate cut-free LK in DAG form.  ...  I would like to thank the anonymous referees for their helpful suggestions which enabled improvement and extention of the results in the first draft of this paper.  ... 
doi:10.1016/0304-3975(95)00193-x fatcat:nhlbyh75jfel3l7du5dgrsgfva

Refutation Of Hard-Determinable Formulas In The System "Resolution Over Linear Equations" And Its Generalization

Anahit Chubaryan
2013 Pure and Applied Mathematics Journal  
R (lin) is the generalization of R (Resolution System) and it is known that many tautologies, which require the exponential lower bounds of proof complexities in R, have polynomially bounded proofs in  ...  We research the power of the propositional proof system R(lin) (Resolution over Linear Equations) described by Ran Raz and Iddo Tzameret.  ...  Acknowledgments This work is supported by grant 11-1b023 of SSC of Goverment of Armenia.  ... 
doi:10.11648/j.pamj.20130203.13 fatcat:cn6egqww4zelbjxewxrqu2hxii

Proof Complexity of Non-classical Logics [chapter]

Olaf Beyersdorff
2010 Lecture Notes in Computer Science  
Traditionally, propositional proofs have been the main object of investigation in proof complexity.  ...  In this paper we give the first survey of this field concentrating on recent developments in proof complexity of non-classical logics. ★ This paper was written while visiting Sapienza University of Rome  ...  Although the first super-polynomial lower bound to the lengths of proofs had already been shown by Tseitin in the late 60's for a sub-system of resolution [Tse68] , the first major achievement in this  ... 
doi:10.1007/978-3-642-13562-0_3 fatcat:kmxntxzltreofhqdixqkrtsylu

Lower bounds for propositional proofs and independence results in bounded arithmetic (abstract) [chapter]

Alexander A. Razborov
1995 Lecture Notes in Computer Science  
We begin with a highly informal discussion of the role played by Bounded Arithmetic and propositional proof systems in the reasoning about the world of feasible computations.  ...  Then we survey some known lower bounds on the complexity of proofs in various propositional proof systems, paying special attention to recent attempts on reducing such bounds to some purely complexity  ...  Notice that if P 0 is polynomially simulated by P 1 then it has a polynomial speed-up over P 1 , that is s P1 ( ) s P0 ( ) O(1) , 2 TAUT C0 .  ... 
doi:10.1007/3-540-60246-1_117 fatcat:4nthzsfwwramnj2bugsxm25rrm

Propositional proof systems and fast consistency provers [article]

Joost J. Joosten
2020 arXiv   pre-print
Next it is proved that fast consistency provers do not exist if one considers RE axiomatized theories rather than theories with an axiom set that is recognizable in polynomial time.  ...  In this paper we define the notion of an unlikely fast consistency prover and prove that its existence is equivalent to NP= coNP.  ...  In this proof, we shall denote by T ⊢ ⋆ ϕ the statement that ϕ is provable in T by a proof whose length is bounded by some polynomial on the (length of) the parameters of ϕ.  ... 
arXiv:2004.05431v1 fatcat:3bgdita2nfa3bhnvpvra4alaze

Propositional Proof Systems and Fast Consistency Provers

Joost J. Joosten
2007 Notre Dame Journal of Formal Logic  
The stay in Prague was also financed by the Netherlands Organization for Scientific Research (NWO).  ...  Krajíček and Pudlák proved in [5] that the existence of an optimal propositional proof system is equivalent to the existence of a fast consistency prover.  ...  In this proof, we shall denote by T ϕ the statement that ϕ is provable in T by a proof whose length is bounded by some polynomial on the (length of) the parameters of ϕ.  ... 
doi:10.1305/ndjfl/1187031410 fatcat:6lkusc3dujbkvbb2dpi2d4roki

Towards NP–P via proof complexity and search

Samuel R. Buss
2012 Annals of Pure and Applied Logic  
This is a survey of work on proof complexity and proof search from a logicoalgorithmic viewpoint, as motivated by the P versus NP problem.  ...  We discuss propositional proof complexity, Cook's program, proof automatizability, proof search, algorithms for satisfiability, and the state of the art of our (in)ability to separate P and NP.  ...  Supported in part by NSF grants DMS-0700533 and DMS-1101228.  ... 
doi:10.1016/j.apal.2011.09.009 fatcat:oud37acsqfgrdio62ir6ci24xi

Are there Hard Examples for Frege Systems? [chapter]

Maria Luisa Bonet, Samuel R. Buss, Toniann Pitassi
1995 Feasible Mathematics II  
The examples of combinatorial tautologies that we consider seem to give at most a quasipolynomial speed-up of extended Frege proofs over Frege proofs, with the sole possible exception of tautologies based  ...  Bondy's theorem is shown to have constant-depth, polynomial-size proofs in Frege+PHP, and to be equivalent in I∆0 to the pigeonhole principle.  ...  In particular, we would like to thank the following people: László Babai, Vašek Chvátal, Stephen Cook, Mauricio Karchmer, Jan Krajíček, Russell Impagliazzo, Steven Rudich, Michael Sipser, Herbert Wilf  ... 
doi:10.1007/978-1-4612-2566-9_3 fatcat:4e2z5jonanfcnj4rqtcwoddjky

Relative efficiency of propositional proof systems: resolution vs. cut-free LK

Noriko H. Arai
2000 Annals of Pure and Applied Logic  
Symbolic Logic 44 (1979) 36 -50 that tree resolution has super-polynomial speed-up over (tree) cut-free LK.  ...  In this paper, we introduce a new algorithm to eliminate atomic cuts and show that cut-free LK (DAG) polynomially simulates resolution when the input formula is expressed as a k-CNF formula.  ...  It was shown that tree resolution has super-polynomial speed-up over analytic tableaux in [8] ; even truth table is more e cient than analytic tableaux on some class of tautologies [10] .  ... 
doi:10.1016/s0168-0072(00)00005-1 fatcat:avrku5jnibh5bfvyzeuhddzpiy

Super-Blocked Clauses [chapter]

Benjamin Kiesl, Martina Seidl, Hans Tompits, Armin Biere
2016 Lecture Notes in Computer Science  
Such procedures identify redundant clauses and faithfully remove them, either before solving in a preprocessing phase or during solving, resulting in a considerable speed up of the SAT solver.  ...  We introduce more powerful generalizations, called set-blocked clauses and super-blocked clauses, respectively.  ...  The k-super-blocking problem is in co-NP for all k ∈ N + . Proof.  ... 
doi:10.1007/978-3-319-40229-1_5 fatcat:qgpj7i4thjdw5kwockiij2777i

Proof Complexity of Non-classical Logics [chapter]

Olaf Beyersdorff, Oliver Kutz
2012 Lecture Notes in Computer Science  
Traditionally, propositional proofs have been the main object of investigation in proof complexity.  ...  In these notes we give an introduction to this recent field of proof complexity of non-classical logics. We cover results from proof complexity of modal, intuitionistic, and non-monotonic logics.  ...  Although the first super-polynomial lower bound to the lengths of proofs had already been shown by Tseitin in the late 60's for a sub-system of Resolution [105] , the first major achievement in this programme  ... 
doi:10.1007/978-3-642-31485-8_1 fatcat:o2gh5kqzp5fpvb3fataonggkz4

Proof Complexity of Propositional Default Logic [chapter]

Olaf Beyersdorff, Arne Meier, Sebastian Müller, Michael Thomas, Heribert Vollmer
2010 Lecture Notes in Computer Science  
In this paper we examine these calculi from a proof-complexity perspective.  ...  In particular, we show that the calculus for credulous reasoning obeys almost the same bounds on the proof size as Gentzen's system LK .  ...  Of course, in the presence of super-polynomial lower bounds to the proof size this cannot be done in polynomial time.  ... 
doi:10.1007/978-3-642-14186-7_5 fatcat:m3j2j4evynb33ljd25w4ot234e
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