Equational Theories of Scattered and Countable Series-Parallel Posets [chapter]

Amrane Amazigh, Nicolas Bedon
2020 Lecture Notes in Computer Science  
In this paper we consider two classes of posets labeled over an alphabet A. The class SP (A) is built from the letters and closed under the operations of series finite, ω and ω products, and finite parallel product. In the class ω SP (A), ω and ω products are replaced by ω and ω powers. We prove that SP (A) and ω SP (A) are freely generated in their respective natural varieties of algebras V and V , and that the equational theory of V is decidable.
doi:10.1007/978-3-030-48516-0_1 fatcat:dtuhf4lzg5dzbdaylbpas2i6t4