The paper presents a design for the Denali-2 super-optimizer, which will generate minimum-instruction-length machine code for realistic machine architectures using automatic theorem-proving technology: specifically, using E-graph matching (a technique for pattern matching in the presence of equality information) and boolean satisfiability solving. The paper presents a precise definition of the ...

We present a tool which allows implicit VDM speciications to be used as search keys for the retrieval of software components. A preprocessing phase utilizes signature matching to lter promising candidates out of a component library. The actual speciication matching phase builds proof obligations from the speciications of key and candidates and feeds them into a theorem prover. Validated obligat...

In this paper we give a proof that the largest set of perfect matchings, in which any two contain a common edge, is the set of all perfect matchings that contain a fixed edge. This is a version of the famous Erdős-Ko-Rado theorem for perfect matchings. The proof given in this paper is algebraic, we first determine the least eigenvalue of the perfect matching derangement graph and use properties...

We consider the well-studied problem of finding a perfect matching in d-regular bipartite graphs with 2n vertices and m = nd edges. While the best-known algorithm for general bipartite graphs (due to Hopcroft and Karp) takes O(m √ n) time, in regular bipartite graphs, a perfect matching is known to be computable in O(m) time. Very recently, the O(m) bound was improved to O(min{m, n 2.5 lnn d })...

Let S be a set of linear inequalities that determine a bounded polyhedron P. The closure of S is the smallest set of inequalities that contains S and is closed under two operations: (i) taking linear combinations of inequalities, (ii) replacing an inequality aj xj ≤ a0, where a1, a2, . . . , an are integers, by the inequality aj xj ≤ a with a ≥ [a0]. Obviously, if integers x1, x2, . . . , xn sa...

We give a simple and short proof for the two ear theorem on matchingcovered graphs which is a well-known result of Lovász and Plummer. The proof relies only on the classical results of Tutte and Hall on the existence of perfect matching in (bipartite) graphs.

We characterize graphs H with the following property: Let G be a graph and F be a subgraph of G such that (i) each component of F is isomorphic to H or K2, (ii) the order of F is maximum. and (iii) the number of H-components in F is minimum subject to (ii). Then a maximum matching of F is also a maximum matching of G. This result is motivated by an analogous property of fractional matching disc...

This paper studies the possibility of strategy-proof rules yielding satisfactory solutions to matching problems. Alcalde and Barberá (1994) show that efficient and individually rational matching rules are manipulable in the one-to-one matching model. We pursue the possibility of strategy-proof matching rules by relaxing efficiency to the weaker condition of respect for unanimity. Our first resu...

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We perform a matching of the two loop-chiral perturbation theory representation of the scalar Kπ form factor to a dispersive one. Knowing the value of FK/Fπ and f+(0) in the Standard Model (SM) allows to determine two O(p) LECs, the slope of the scalar form factor and the deviation of the Callan-Treiman theorem. Going beyond the SM and assuming the knowledge of the slope of the scalar form fact...