This paper introduces a notion of equivalence for higher-dimensional automata, called weak equivalence. Weak equivalence focuses mainly on a traditional trace language and a new homology language, which captures the overall independence structure of an HDA. It is shown that weak equivalence is compatible with both the tensor product and the coproduct of HDAs and that, under certain conditions, HDAs may be reduced to weakly equivalent smaller ones by merging and collapsing cubes.
- Pub Date:
- October 2019
- Computer Science - Logic in Computer Science;
- Computer Science - Formal Languages and Automata Theory;
- Mathematics - Algebraic Topology;
- Discrete Mathematics &