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A pair of closed form functions (F,G) is said to be a Wilf-Zeilberger pair if F(n+1,k)-F(n,k)=G(n,k+1)-G(n,k). (1) The Wilf-Zeilberger formalism provides succinct proofs of ...

A shortest path between two graph vertices (u,v) of a graph (Skiena 1990, p. 225). There may be more than one different shortest paths, all of the same length. Graph ...

A cipher is an algorithm that converts data (plaintext) to an obfuscated form that is not directly readable. Ciphers are usually used with the intention of hiding the ...

A function H that maps an arbitrary length message M to a fixed length message digest MD is a collision-free hash function if 1. It is a one-way hash function. 2. It is hard ...

The complexity of a process or algorithm is a measure of how difficult it is to perform. The study of the complexity of algorithms is known as complexity theory. In general, ...

Does there exist an algorithm for deciding whether or not a specific mathematical assertion does or does not have a proof? The decision problem is also known as the ...

The inversion of a convolution equation, i.e., the solution for f of an equation of the form f*g=h+epsilon, given g and h, where epsilon is the noise and * denotes the ...

Let f(x) be a monic polynomial of degree d with discriminant Delta. Then an odd integer n with (n,f(0)Delta)=1 is called a Frobenius pseudoprime with respect to f(x) if it ...

Let V(G) be the vertex set of a simple graph and E(G) its edge set. Then a graph isomorphism from a simple graph G to a simple graph H is a bijection f:V(G)->V(H) such that ...

There exists no known P algorithm for graph isomorphism testing, although the problem has also not been shown to be NP-complete. In fact, the problem of identifying ...