It has been proven that extended resolution (ER) more powerful reasoning than general for the pigeonhole principle in Cook’s paper. This fact indicates possibility a solver based on can exceed Boolean satisfiability problem solvers (SAT short) resolution. However, few studies have provided practical evidence of this assumption. paper explores how improve SAT by using principle, which was first ...

The resolution complexity of the perfect matching principle was studied by Razborov [14], who developed a technique for proving its lower bounds for dense graphs. We construct a constant degree bipartite graph Gn such that the resolution complexity of the perfect matching principle for Gn is 2 where n is the number of vertices in Gn. This lower bound is tight up to some polynomial. Our result i...

We consider exponentially large finite relational structures (with the universe {0, 1}) whose basic relations are computed by polynomial size (n) circuits. We study behaviour of such structures when pulled back by P/polymaps to a bigger or to a smaller universe. In particular, we prove that: 1. If there exists a P/poly map g : {0, 1} → {0, 1} , n < m, iterable for a proof system then a tautolog...

We study the extension (introduced as BT in [5]) of the theory S 2 by instances of the dual (onto) weak pigeonhole principle for p-time functions, dWPHP(PV )x2 . We propose a natural framework for formalization of randomized algorithms in bounded arithmetic, and use it to provide a strengthening of Wilkie’s witnessing theorem for S 2+dWPHP(PV ). We construct a propositional proof system WF (bas...

The principle sPHPb (PV (α)) states that no oracle circuit can compute a surjection of a onto b. We show that sPHP P (a)(PV (α)) is independent of PV1(α)+ sPHP π(a) Π(a)(PV (α)) for various choices of the parameters π, Π, %, P . We also improve the known separation of iWPHP(PV ) from S 2 + sWPHP(PV ) under cryptographic assumptions.

For each p 2 there exists a model M of I 0 () which satisses the Count(p) principle. Furthermore, if p contains all prime factors of q there exist n; r 2 M and a bijective map f 2 dom(M) mapping f1; 2 A corollary is a complete classiication of the Count(q) versus Count(p) problem. Another corollary shows that the pigeonhole principle for injective maps does not follow from any of the Count(q) p...

We present a simple and completely model-theoretical proof of a strengthening of a theorem of Ajtai's: the independence of the pigeonhole principle from I 0 (R). Qua strength, the theorem proved here corresponds to the complexity/proof-theoretical results of 10] and 14] but a diierent combinatorics is used. Techniques inspired by Razborov 11] replace those derived from H astad 8]. This leads to...

The next-generation sequencing (NGS) technology outputs a huge number of sequences (reads) that require further processing. After applying prefiltering techniques in order to eliminate redundancy and to correct erroneous reads, an overlap-based assembler typically finds the longest exact suffix-prefix match between each ordered pair of the input reads. However, another trend has been evolving f...

A typical result in (additive) Ramsey theory takes the following form: if N (or {1, . . . , N} with N sufficiently large) is partitioned into finitely many classes, then at least one of these classes will contain contain a specific arithmetic structure (e.g. an arithmetic progression). The simplest example of such a result is the pigeonhole principle and one can view Ramsey theory as the study ...