We present the general Hardy-like quantum pigeonhole paradoxes for \textit{n}-particle states, and find that each of such can be simply associated to an un-colorable solution a specific vertex-coloring problem induced from projected-coloring graph (a kind unconventional graph). Besides, as special Hardy's paradox, several kinds even give rise higher success probability in demonstrating conflict...

The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the resolution proof system, for which many hard examples exist. This paper proposes a new problem transformation, which enables reducing the decision problem for for...

Many leading-edge SAT solvers are based on the Davis-Putnam procedure or the Davis-Logemann-Loveland procedure, and thus on unsatisfiable instances they can be viewed as attempting to find refutations by resolution. Therefore, exponential lower bounds on the length of resolution proofs also apply to such solvers. Empirical performance of DLL-based solvers on SAT instances from the pigeonhole an...

Proofs in propositional logic are typically presented as trees of derived formulas or, alternatively, directed acyclic graphs formulas. This distinction between tree-like vs. dag-like structure is particularly relevant when making quantitative considerations regarding, for example, proof size. Here we analyze a more general type structural restriction proofs rule-based systems. In this definiti...

As proved first by HENSON in [4], the countable random graph R (also called the countable universal homogeneous graph) has the following unusual property: if the vertices of R are partitioned into finitely many sets XI,. . ,X,, then for some 1 5 i 5 n the induced subgraph on Xi is isomorphic to R. CAMERON (see [l] and [2]) has called this property the pigeonhole proper t y . One can generalize ...

This paper describes the LINA system for the BUCC 2015 shared track. Following (Enright and Kondrak, 2007), our system identify comparable documents by collecting counts of hapax words. We extend this method by filtering out document pairs sharing target documents using pigeonhole reasoning and cross-lingual information.

The schematic CERES method [?] is a recently developed method of cut elimination for proof schemata, that is a sequence of proofs with a recursive construction. Proof schemata can be thought of as a way to circumvent adding an induction rule to the LK-calculus. In this work, we formalize a schematic version of the infinitary pigeonhole principle, which we call the Non-injectivity Assertion sche...

We answer a question of P. Cameron’s by giving examples of 2א0 many non-isomorphic acyclic orientations of the infinite random graph with a topological ordering that do not have the pigeonhole property. Our examples also embed each countable linear ordering. A graph is n-existentially closed or n-e.c. if for each n-subset S of vertices, and each subset T of S (possibly empty), there is a vertex...

After giving some background on sums of residue classes we explained the following problem on multidimensional zero sums which is well known in combinatorial number theory: Let f(n, d) denote the least integer such that any choice of f(n, d) elements in Zn contains a subset of size n whose sum is zero. Harborth [12] proved that (n − 1)2 + 1 ≤ f(n, d) ≤ (n − 1)n + 1. The lower bound follows from...