Higher-dimensional Delta-systems

Higher Dimensional Transition Systems

We introduce the notion of higher dimensional transition systems as a model of concurrency providing an elementary, set-theoretic formalisation of the idea of higher dimensional transition. We show an embedding of the category of higher dimensional transition systems into that of higher dimensional automata which cuts down to an equivalence when we restrict to non-degenerate automata. Moreover,...

Higher Dimensional Recursive Matrices and Diagonal Delta Sets of Series

The idea to study infinite matrices whose entries are the coefficients of the powers of a given formal series is rather old and dates back at least to Schur’s posthumous papers on Faber polynomials [39-41]. In 1953, Jabotinsky reconsidered Schur and Shiffer’s [38] work on the subject and developed a systematic study of these matrices [20]. Since then, several applications confirmed that Jabotin...

Higher-dimensional automata modeling shared-variable systems

The purpose of this paper is to provide a construction to model shared-variable systems using higher-dimensional automata which is compositional in the sense that the parallel composition of completely independent systems is modeled by the standard tensor product of HDAs and nondeterministic choice is represented by the coproduct.

Delta and Singular Delta Locus for One Dimensional Systems of Conservation Laws

A condition for existence of singular and delta shock waves for systems of conservation laws is given in the paper. The systems considered here have fluxes which are linear in one of the dependent variables. The condition obtained here is analogous to the one for the standard Hugoniot locus. Three different solution concept are used in the paper: associated solution in Colombeau sense, limits o...

Higher Dimensional