EMSO-logic and automata related to homogeneous flow event structures

Abstract

In this paper we study the recognizability and definability on existential monadic second order (EMSO) logic of languages related to homogeneous flow event structures (HFES), i.e., the languages of configurations (posets) and the languages of proving sequences (words). An HFES is specified by an arbitrary poset G = (V,⩽) and a finite FES F as a result of copying F in vertices of G with additional homogeneous flow and conflict relations on the events of adjacent vertices. The problem is: whether the sets of configurations of HFES and languages of proving sequences are EMSO-definable. Results refer to the domains of linear orders, binary trees, and two-dimensional grids. If G is the domain of linear order or binary tree then the recognizability and EMSO-definability of configurations of HFES hold. We give some classes of HFES where the recognizability does not hold for the two-dimensional grid. The EMSO-definability of proving sequences is proved for all considered classes of HFES.