This paper explores the algebraic matching approach for detection of vulnerabilities in binary codes. The algebraic programming system is used for implementing this method. It is anticipated that models of vulnerabilities and programs to be verified are presented as behavior algebra and action language specifications. The methods of algebraic matching are based on rewriting rules and techniques...

Animation of execution is a necessary feature of source level debuggers We present a framework where animators are generated from existing algebraic speci cations of interpreters To this end a pattern matching mechanism is used in conjunction with origin tracking a generic tracing technique The generation of animators is illustrated using an example language named CLaX a Pascal relative We stud...

Tutte introduced a V by V skew-symmetric matrix T = (tij), called the Tutte matrix, associated with a simple graph G= (V,E). He associates an indeterminate ze with each e ∈ E, then defines tij = ±ze when ij = e ∈ E, and tij = 0 otherwise. The rank of the Tutte matrix is exactly twice the size of a maximum matching of G. Using linear algebra and ideas from the Gallai–Edmonds decomposition, we de...

Given a set of nodes and edges between them, what’s the maximum of number of disjoint edges? This problem is known as the graph matching problem, and its study has had an enormous impact on the develpoment of algorithms, combinatorics, optimization theory, and even complexity theory. Mathematicians have been interested in the matching problem since the 19th century, leading to celebrated theore...

The decidability of algebraic higher-order matching is proved. Algebraic higher-order matching is a matching where the constant term in equation is built of first-order constants and constants of a base type. This result is particularly appealing in the light of the last result of Loader.

The number of vertices missed by a maximum matching in a graph G is the multiplicity of zero as a root of the matchings polynomial μ(G,x) of G, and hence many results in matching theory can be expressed in terms of this multiplicity. Thus, if mult(θ,G) denotes the multiplicity of θ as a zero of μ(G,x), then Gallai’s lemma is equivalent to the assertion that if mult(θ,G\u) < mult(θ,G) for each v...

GADTs, short for Generalized Algebraic DataTypes, which allow constructors of algebraic datatypes to be non-surjective, have many useful applications. However, pattern matching on GADTs introduces local type equality assumptions, which are a source of ambiguities that may destroy principal types— and must be resolved by type annotations. We introduce ambivalent types to tighten the definition o...