In many security protocols, such as group protocols, principals have to perform iterative or recursive computations. We call such protocols recursive protocols. Recently, first results on the decidability of the security of such protocols have been obtained. While recursive protocols often employ operators with algebraic, security relevant properties, such as the exclusive OR (XOR), the existin...

Combinatorial objects such as rooted trees that carry a recursive structure have found important applications recently in both mathematics and physics. We put such structures in an algebraic framework of operated semigroups. This framework provides the concept of operated semigroups with intuitive and convenient combinatorial descriptions, and at the same time endows the familiar combinatorial ...

In this extended abstract, we present the first combinatorial scheme for counting labeled 4-regular planar graphs through a complete recursive decomposition. More precisely, we show that the exponential generating function counting labeled 4regular planar graphs can be computed effectively as the solution of a system of equations. From here we can extract the coefficients by means of algebraic ...

Algebraic space–time coding allows for reliable data exchange across fading multiple-input multiple-output channels. A powerful technique for decoding space–time codes is Maximum-Likelihood (ML) decoding, but well-performing and widely-used codes such as the Golden code often suffer from high ML-decoding complexity. In this article, a recursive algorithm for decoding general algebraic space–tim...

We present a semi-decision procedure for checking satisfiability of formulas in the language of algebraic data types and integer linear arithmetic extended with user-defined terminating recursive functions. Our procedure is designed to integrate into a DPLL(T ) solver loop, using blocking clauses to control function definition unfolding. The procedure can check the faithfulness of candidate cou...

HipSpec is a system for automatically deriving and proving properties about functional programs. It uses a novel approach, combining theory exploration, counterexample testing and inductive theorem proving. HipSpec automatically generates a set of equational theorems about the available recursive functions of a program. These equational properties make up an algebraic specification for the prog...

(A) The generating functions for the 12j and 15j coefficients are explicitly computed in the Bargmann scheme. It is a tribute to the powerful Bargmann lemmas on the Laplacian integrals4 that those seemingly complicated 6n-fold integrals can in fact be systematically carried out. Thus in prinCiple the generating functions for the 3nj coefficients are computable for arbitrary n in the Bargmann ap...

following the categorical approach to universal algebra through algebraic theories, proposed by f.~w.~lawvere in his phd thesis, this paper aims at introducing a similar setting for general topology. the cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. we introduce t...

This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The overall assumptions needed are small indeed: working only in categories with “enough final coalgebras” we show how to formulate, solve, and study recursive p...

Repeat-Accumulate (RA) codes, consisting of a simple binary repetition followed by a permutation and an accumulator, are converting into quasi-cyclic codes with multiple cross-linked cycles. The algebraic heuristics are used to design codes with an explicit algebraic permutation yielding desirable graph properties. Recursive graph constructions techniques are given for the construction of very ...