For predual categories C andD we establish isomorphisms between opfibrations representing local varieties of languages in C, local pseudovarieties of D-monoids, and finitely generated profinite D-monoids. The global sections of these opfibrations are shown to correspond to varieties of languages in C, pseudovarieties of D-monoids, and profinite equational theories of D-monoids, respectively. As...

In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis. In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum games. The simple case of one-player games is strongly related to automata theory on infinite words. All along the article, we focus on general approaches to so...

In this paper, we will investigate two partial orders on classical states∆n that induce a domain theoretic structure. In particular, we will look at the Bayesian order presented by Coecke and Martin (2002) and the implicative order presented by Martin (2004). For both of the domains that arise from these orderings on the classical states, Shannon entropy is a measurement in the domain theoretic...

The classical theory of deterministic automata is presented in terms of the notions of homomorphism and bisimulation, which are the cornerstones of the theory of (universal) coalgebra. This leads to a transparent and uniform presentation of automata theory and yields some new insights, amongst which coinduction proof methods for language equality and language inclusion. At the same time, the pr...

This paper proposes a framework which unifies graphical model theory and formal language theory through automata theory. Specifically, we propose Bayesian Network Automata (BNAs) as a formal framework for specifying graphical models of arbitrarily large structures, or equivalently, specifying probabilistic grammars in terms of graphical models. BNAs use a formal automaton to specify how to cons...

We propose a modeling and analysis method for biochemical reactions based on finite state automata. This is a completely different approach compared to traditional modeling of reactions by differential equations. Our method aims to explore the algebraic structure behind chemical reactions using automatically generated coordinate systems. In this paper we briefly summarize the underlying mathema...

This paper is a self-contained introduction to the theory of finite-state automata on infinite words. The study of automata on infinite inputs was initiated by Büchi in order to settle certain decision problems arising in logic. Subsequently, there has been a lot of fundamental work in this area, resulting in a rich and elegant mathematical theory. In recent years, there has been renewed intere...

The emerging field of Nominal Computation Theory is concerned with the theory of Nominal Sets and its applications to Computer Science. We investigate here the impact of nominal sets on the definition of Cellular Automata and on their computational capabilities, with a special focus on the emergent behavioural properties of this new model and their significance in the context of computationorie...

Cellular automata are classes of mathematical systems characterized by discreteness (in space, time, and state values), determinism, and local interaction. Using symbolic dynamical theory, we coarse-grain the temporal evolution orbits of cellular automata. By means of formal languages and automata theory, we study the evolution complexity of the elementary cellular automaton with local rule num...

This paper presents one-stack automata as acceptors of context-free languages; these are equivalent to Pushdown Automata which are well known in automata theory. As equivalence relations such as equivalence of Turing Machines and two-stack Pushdown Automata help in learning general properties of formal modeling, the equivalence relation of Pushdown Automata and one-stack automata also helps in ...