Space in Weak Propositional Proof Systems

2017 ◽  
Author(s):  
Ilario Bonacina
Keyword(s):  
Proof Systems ◽  
Propositional Proof Systems ◽  
Propositional Proof

Disjoint NP-Pairs and Propositional Proof Systems

2014 ◽  
Vol 45 (4) ◽  
pp. 59-75 ◽  
Author(s):  
C. Glaßer ◽  
A. Hughes ◽  
A. L. Selman ◽  
N. Wisiol
Keyword(s):  
Proof Systems ◽  
Propositional Proof Systems ◽  
Propositional Proof

ON NON-MONOTONOUS PROPERTIES OF SOME CLASSICAL AND NONCLASSICAL PROPOSITIONAL PROOF SYSTEMS

2020 ◽  
Vol 54 (3 (253)) ◽  
pp. 127-136
Author(s):  
Anahit A. Chubaryan ◽  
Arsen A. Hambardzumyan
Keyword(s):  
Cut Rule ◽  
Proof Systems ◽  
Nonclassical Logics ◽  
Frege Systems ◽  
Sequent Systems ◽  
Propositional Proof Systems ◽  
Propositional Proof

We investigate the relations between the proof lines of non-minimal tautologies and its minimal tautologies for the Frege systems, the sequent systems with cut rule and the systems of natural deductions of classical and nonclassical logics. We show that for these systems there are sequences of tautologies ψn, every one of which has unique minimal tautologies φn such that for each n the minimal proof lines of φn are an order more than the minimal proof lines of ψn.

Propositional proof systems, the consistency of first order theories and the complexity of computations

1989 ◽  
Vol 54 (3) ◽  
pp. 1063-1079 ◽  
Author(s):  
Jan Krajíček ◽  
Pavel Pudlák
Keyword(s):  
First Order ◽  
Proof Systems ◽  
Propositional Proof Systems ◽  
Propositional Proof

AbstractWe consider the problem about the length of proofs of the sentences saying that there is no proof of contradiction in S whose length is < n. We show the relation of this problem to some problems about propositional proof systems.

scholarly journals THE INFORMATIONAL CONTENT OF CANONICAL DISJOINT NP-PAIRS

2009 ◽  
Vol 20 (03) ◽  
pp. 501-522 ◽  
Author(s):  
CHRISTIAN GLAßER ◽  
ALAN L. SELMAN ◽  
LIYU ZHANG
Keyword(s):  
Open Problem ◽  
Structural Complexity ◽  
Informational Content ◽  
Proof Systems ◽  
Canonical Pair ◽  
Propositional Proof Systems ◽  
Np Complete ◽  
Complete Sets ◽  
Propositional Proof ◽  
Almost All

We investigate the connection between propositional proof systems and their canonical pairs. It is known that simulations between propositional proof systems translate to reductions between their canonical pairs. We focus on the opposite direction and study the following questions. Q1: For which propositional proof systems f and g does the implication [Formula: see text] hold, and for which does it fail? Q2: For which propositional proof systems of different strengths are the canonical pairs equivalent? Q3: What do (non-)equivalent canonical pairs tell about the corresponding propositional proof systems? Q4: Is every NP-pair (A, B), where A is NP-complete, strongly many-one equivalent to the canonical pair of some propositional proof system? In short, we show that Q1 and Q2 can be answered with 'for almost all', which generalizes previous results by Pudlák and Beyersdorff. Regarding Q3, inequivalent canonical pairs tell that the propositional proof systems are not "very similar," while equivalent, P -inseparable canonical pairs tell that they are not "very different." We can relate Q4 to the open problem in structural complexity that asks whether unions of disjoint NP-complete sets are NP-complete. This demonstrates a new connection between propositional proof systems, disjoint NP-pairs, and unions of disjoint NP-complete sets.

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