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Electronic Colloquium on Computational Complexity

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Reports tagged with Propositional Proof System:
TR98-035 | 8th May 1998
Maria Luisa Bonet, Juan Luis Esteban, Jan Johannsen

Exponential Separations between Restricted Resolution and Cutting Planes Proof Systems

We prove an exponential lower bound for tree-like Cutting Planes
refutations of a set of clauses which has polynomial size resolution
refutations. This implies an exponential separation between tree-like
and dag-like proofs for both Cutting Planes and resolution; in both
cases only superpolynomial separations were known before.
In order to ... more >>>

TR01-011 | 21st January 2001
Dima Grigoriev, Edward Hirsch

Algebraic proof systems over formulas

We introduce two algebraic propositional proof systems F-NS
and F-PC. The main difference of our systems from (customary)
Nullstellensatz and Polynomial Calculus is that the polynomials
are represented as arbitrary formulas (rather than sums of
monomials). Short proofs of Tseitin's tautologies in the
constant-depth version of F-NS provide ... more >>>

TR01-103 | 14th December 2001
Dima Grigoriev, Edward Hirsch, Dmitrii V. Pasechnik

Complexity of semi-algebraic proofs

Revisions: 3

It is a known approach to translate propositional formulas into
systems of polynomial inequalities and to consider proof systems
for the latter ones. The well-studied proof systems of this kind
are the Cutting Planes proof system (CP) utilizing linear
inequalities and the Lovasz-Schrijver calculi (LS) utilizing
quadratic ... more >>>

TR03-055 | 20th July 2003
Jan Krajicek

Implicit proofs

We describe a general method how to construct from
a propositional proof system P a possibly much stronger
proof system iP. The system iP operates with
exponentially long P-proofs described ``implicitly''
by polynomial size circuits.

As an example we prove that proof system iEF, implicit EF,
corresponds to bounded ... more >>>

TR05-006 | 28th December 2004
Edward Hirsch, Sergey I. Nikolenko

Simulating Cutting Plane proofs with restricted degree of falsity by Resolution

Comments: 1

Goerdt (1991) considered a weakened version of the Cutting Plane proof system with a restriction on the degree of falsity of intermediate inequalities. (The degree of falsity of an inequality written in the form $\sum a_ix_i+\sum b_i(1-x_i)\ge c,\ a_i,b_i\ge0$ is its constant term $c$.) He proved a superpolynomial lower bound ... more >>>

TR10-193 | 5th December 2010
Edward Hirsch, Dmitry Itsykson, Ivan Monakhov, Alexander Smal

On optimal heuristic randomized semidecision procedures, with applications to proof complexity and cryptography

The existence of an optimal propositional proof system is a major open question in proof complexity; many people conjecture that such systems do not exist. Krajicek and Pudlak (1989) show that this question is equivalent to the existence of an algorithm that is optimal on all propositional tautologies. Monroe (2009) ... more >>>

TR19-050 | 20th March 2019
Titus Dose, Christian Gla├čer

NP-Completeness, Proof Systems, and Disjoint NP-Pairs

The article investigates the relation between three well-known hypotheses.
1) Hunion: the union of disjoint complete sets for NP is complete for NP
2) Hopps: there exist optimal propositional proof systems
3) Hcpair: there exist complete disjoint NP-pairs

The following results are obtained:
a) The hypotheses are pairwise independent ... more >>>

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