Using classical automata theory we show how noninterference can be viewed as a relatively simple phenomenon. We also give direction for future work concerning probabilistic security problems using classical automata theory.

Kleene algebra with tests is an extension of Kleene algebra, the algebra of regular expressions, which can be used to reason about programs. We develop a coalgebraic theory of Kleene algebra with Tests, along the lines of the coalgebraic theory of regular expressions based on deterministic automata. Since the known automata-theoretic presentation of Kleene algebra with tests does not lend itsel...

These lecture notes will develop the method of binary decision diagrams – a technique for representing Boolean functions – from automata theory. We include a compact presentation of automata theory required for the purpose, and indicate applications.

Motivated by Ying’ work on automata theory based on quantum logic (Ying, M. S. (2000). International Journal of Therotical Physics, 39(4): 985–996; 39(11): 2545– 2557) and inspired by the close relationship between the automata theory and the theory of formal grammars, we have established a basic framework of grammar theory on quantum logic and shown that the set of l-valued quantum regular lan...

DNA computers provide new paradigms of computing (Păun et al., 1998). They appeared at the end of the last century. In contrast, the theory of finite automata is well developed and intensively used in both theory and practice. The Watson-Crick automata, introduced in (Freund et al., 1997), relate to both fields. They are important in the field of (DNA) computing and have important relation to f...

We extend the classical Stallings theory (describing subgroups of free groups as automata) to direct products and abelian groups: after introducing enriched automata (i.e., with extra labels), we obtain an explicit bijection between a certain type such automata, which - it happens in group is computable finitely generated case. This approach provides neat geometric description (even non gener...

Two formalisms for concurrency, the Input Output automaton model and the theory of testing, are compared and are shown to have common foundations. The relationship between the fair and quiescent preorders of I O automata is investigated and the two preorders are shown to coincide subject to some restrictions. I O automata are encoded into the theory of testing and the reversed must preorder is ...

We present a compositional algebraic framework to describe the evolution of quantum fields in discretised spacetimes. show how familiar notions from Relativity and causality can be recovered purely order-theoretic way causal order events spacetime, with no direct mention analysis or topology. formulate theory-independent over orders compositional, functorial way. draw strong connection Algebrai...

This paper is a survey on the algebraic approach to the theory of automata accepting infinite words. We discuss the various acceptance modes (Büchi automata, Muller automata, transition automata, weak recognition by a finite semigroup, ω-semigroups) and prove their equivalence. We also give two algebraic proofs of McNaughton’s theorem on the equivalence between Büchi and Muller automata. Finall...

We describe in terms of automata theory the automatic actions with post-critically finite limit space. We prove that these actions are precisely the actions by bounded automata and that any self-similar action by bounded automata is contracting.