Good Degree Bounds on Nullstellensatz Refutations of the Induction Principle
Samuel R. Buss,Toniann Pitassi +1 more
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This paper gives nearly optimal, logarithmic upper and lower bounds on the minimum degree of Nullstellensatz refutations (i.e., polynomials) of the propositional induction principle.About:
This article is published in Journal of Computer and System Sciences.The article was published on 1998-10-01 and is currently open access. It has received 26 citations till now. The article focuses on the topics: Upper and lower bounds & Degree (graph theory).read more
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DissertationDOI
Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization
TL;DR: In this paper, the authors introduce a specific class of linear matrix inequalities (LMI) whose optimal solution can be characterized exactly, i.e., the optimal value equals the spectral radius of the operator.
Journal ArticleDOI
The complexity of propositional proofs
TL;DR: A broad survey of the field, and a technical exposition of some recently developed techniques for proving lower bounds on proof sizes are included.
Journal ArticleDOI
Linear gaps between degrees for the polynomial calculus modulo distinct primes
TL;DR: In this article, the Tseitin mod p principles, TS/sub n/(p), are translated MOD/sub p/sup n/ polynomials into the Fourier basis.
Proceedings ArticleDOI
Lifting Nullstellensatz to monotone span programs over any field
Toniann Pitassi,Robert Robere +1 more
TL;DR: In this article, the size of monotone span programs over arbitrary fields was characterized by the Nullstellensatz degree of a related unsatisfiable Boolean formula, which yields the first exponential lower bounds for such programs.
Proceedings ArticleDOI
Hilbert's nullstellensatz and an algorithm for proving combinatorial infeasibility
TL;DR: An algorithm aimed at proving combinatorial infeasibility based on the observed low degree of Hilbert's Nullstellensatz certificates for polynomial systems arising in combinatorics and on large-scale linear-algebra computations over K is investigated.
References
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The intractability of resolution
TL;DR: It is proved that, for infinitely many disjunctive normal form propositional calculus tautologies ξ, the length of the shortest resolution proof of ξ cannot be bounded by any polynomial of the lengthof ξ.
Proceedings ArticleDOI
Using the Groebner basis algorithm to find proofs of unsatisfiability
TL;DR: It is shown that the Groebner system polynomially simulates Horn clause resolution, quasi-polynomially simulating tree-like resolution, and weakly exponentially simulates resolution will have better than worst-case behaviour on the same classes of inputs that resolution does.
Journal ArticleDOI
Sharp effective Nullstellensatz
TL;DR: Brownawell as mentioned in this paper used elimination theory to get a bound on the degree of the gi's which was doubly exponential in the number of variables, which was later improved in [MW] and in [Th].
Proceedings ArticleDOI
Lower bounds on Hilbert's Nullstellensatz and propositional proofs
TL;DR: The technique enables us to extend the independence results for counting principles to composite numbers p and q and results in an exact characterization of when Count/sub q/ can be proven efficiently from Count/ sub p/, for all p andq.