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540
The Deduction Rule and Linear and Nearlinear Proof Simulations
"... ... that a Frege proof of n lines can be transformed into a treelike Frege proof of O(n log n) lines and of height O(log n). As a corollary of this fact we can prove that natural deduction and sequent calculus treelike systems simulate Frege systems with proof lengths bounded by O(n log n). ..."
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Cited by 12 (5 self)
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... that a Frege proof of n lines can be transformed into a treelike Frege proof of O(n log n) lines and of height O(log n). As a corollary of this fact we can prove that natural deduction and sequent calculus treelike systems simulate Frege systems with proof lengths bounded by O(n log n).
Lifting Lower Bounds for TreeLike Proofs
, 2011
"... It is known that constantdepth Frege proofs of some tautologies require exponential size. No such lower bound result is known for more general proof systems. We consider treelike Sequent Calculus proofs in which formulas can contain modular connectives and only the cut formulas are restricted to b ..."
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It is known that constantdepth Frege proofs of some tautologies require exponential size. No such lower bound result is known for more general proof systems. We consider treelike Sequent Calculus proofs in which formulas can contain modular connectives and only the cut formulas are restricted
Upper and Lower Bounds for Treelike Cutting Planes Proofs
 In 9th IEEE Symposium on Logic in Computer Science
, 1994
"... In this paper we study the complexity of Cutting Planes (CP) refutations, and treelike CP refutations. Treelike CP proofs are natural and still quite powerful. In particular, the propositional pigeonhole principle (PHP) has been shown to have polynomialsized treelike CP proofs. Our main result s ..."
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Cited by 40 (8 self)
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sized Frege proofs, it follows that treelike CP cannot polynomially simulate Frege systems. 1 Introduction An important open problem is to determine whether there exists a propositional proof system that admits short (polynomial size) proofs for all tautologies, or equivalently, whether or not NP equals co
Quantified Propositional Logic and the Number of Lines of TreeLike Proofs
, 1999
"... There is an exponential speedup in the number of lines of the quantified propositional sequent calculus over Substitution Frege Systems, if one considers proofs as trees. Whether this is true also for the number of symbols, is still an open problem. 1 Some background The existence of a proposi ..."
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There is an exponential speedup in the number of lines of the quantified propositional sequent calculus over Substitution Frege Systems, if one considers proofs as trees. Whether this is true also for the number of symbols, is still an open problem. 1 Some background The existence of a
Number of symbols in Frege proofs with and without the deduction rule
, 2004
"... Frege systems with the deduction rule produce at most quadratic speedup over Frege systems using as a measure of length the number of symbols in the proof. We study whether that speedup is in reality smaller. We show that the speedup is linear when the Frege proofs are treelike. Also, two groups o ..."
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Cited by 6 (0 self)
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Frege systems with the deduction rule produce at most quadratic speedup over Frege systems using as a measure of length the number of symbols in the proof. We study whether that speedup is in reality smaller. We show that the speedup is linear when the Frege proofs are treelike. Also, two groups
Treelike tableaux
 IN 23RD INTERNATIONAL CONFERENCE ON FORMAL POWER SERIES AND ALGEBRAIC COMBINATORICS (FPSAC 2011), DISCRETE MATH. THEOR. COMPUT. SCI. PROC., AO:63–74
, 2011
"... In this work we introduce and study treelike tableaux, which are certain fillings of Ferrers diagrams in simple bijection with permutation tableaux and alternative tableaux. We exhibit an elementary insertion procedure on our tableaux which gives a clear proof that tableaux of size n are counted ..."
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Cited by 8 (1 self)
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In this work we introduce and study treelike tableaux, which are certain fillings of Ferrers diagrams in simple bijection with permutation tableaux and alternative tableaux. We exhibit an elementary insertion procedure on our tableaux which gives a clear proof that tableaux of size n are counted
Separating daglike and treelike proof systems
 Accepted in LICS
, 2007
"... We show that treelike (Gentzen’s calculus) PK where all cut formulas have depth at most a constant d does not simulate cutfree PK. Generally, we exhibit a family of sequents that have polynomial size cutfree proofs but requires superpolynomial treelike proofs even when the cut rule is allowed on ..."
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Cited by 4 (1 self)
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We show that treelike (Gentzen’s calculus) PK where all cut formulas have depth at most a constant d does not simulate cutfree PK. Generally, we exhibit a family of sequents that have polynomial size cutfree proofs but requires superpolynomial treelike proofs even when the cut rule is allowed
Linear lower bounds and simulations in Frege systems with substitutions
, 1997
"... We investigate the complexity of proofs in Frege (F), Substitution Frege (sF) and Renaming Frege (rF) systems. Starting from a recent work of Urquhart and using Kolmogorov Complexity we give a more general framework to obtain superlogarithmic lower bounds for the number of lines in both treelike an ..."
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We investigate the complexity of proofs in Frege (F), Substitution Frege (sF) and Renaming Frege (rF) systems. Starting from a recent work of Urquhart and using Kolmogorov Complexity we give a more general framework to obtain superlogarithmic lower bounds for the number of lines in both treelike
TreeLike Resolution Is Superpolynomially Slower Than DAGLike Resolution for the Pigeonhole Principle
 In Proceedings of the 10th International Symposium on Algorithms and Computation (ISAAC
, 1999
"... . Our main result shows that a shortest proof size of treelike resolution for the pigeonhole principle is superpolynomially larger than that of DAGlike resolution. In the proof of a lower bound, we exploit a relationship between treelike resolution and backtracking, which has long been recognized ..."
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Cited by 7 (0 self)
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. Our main result shows that a shortest proof size of treelike resolution for the pigeonhole principle is superpolynomially larger than that of DAGlike resolution. In the proof of a lower bound, we exploit a relationship between treelike resolution and backtracking, which has long been
On Frege and Extended Frege Proof Systems
, 1993
"... We propose a framework for proving lower bounds to the size of EF  proofs (equivalently, to the number of proofsteps in Fproofs) in terms of boolean valuations . The concept is motivated by properties of propositional provability in models of bounded arithmetic and it is a finitisation of a parti ..."
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Cited by 21 (4 self)
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We propose a framework for proving lower bounds to the size of EF  proofs (equivalently, to the number of proofsteps in Fproofs) in terms of boolean valuations . The concept is motivated by properties of propositional provability in models of bounded arithmetic and it is a finitisation of a
Results 1  10
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540