Abstract not found

This paper gives an equational axiomatization of probabilistic bisimulation equivalence for a class of finite-state agents previously studied by Stark and Smolka ((2000) Proof, Language, and Interaction: Essays in Honour of Robin Milner, pp. 571-595). The axiomatization is obtained by extending the general axioms of iteration theories (or iteration algebras), which characterize the equational properties of the fixed point operator on (#-)continuous or monotonic functions, with three axiom schemas that express laws that are specific to probabilistic bisimilarity.

We present a new approach for expressing and solving boundary problems for linear ordinary differential equations in the language of differential algebras. Starting from an algebra with a derivation and integration operator, we construct a ring of linear integro-differential operators that is expressive enough for specifying regular boundary problems with arbitrary Stieltjes boundary conditions as well as their solution operators. Based on these structures, we define a new multiplication on regular boundary problems in such a way that the resulting Green’s operator is the reverse composition of the constituent Green’s operators. We provide also a method for lifting any factorization of the underlying differential operator to the level of boundary problems. Since this method only needs the computation of initial value problems, it can be used as an effective alternative for computing Green’s operators in case one knows how to factor the given differential operators.

A group automaton is a complete deterministic automaton such that each letter of the alphabet acts on the set of states as a permutation [1, 5]. The aim is to describe an algorithm for the random generation of a minimal group automaton with n states. The treatment is largely based on properties of random permutations and random automata. 1. Properties A group automaton is a complete deterministic automaton such that each letter of the alphabet acts on the set of states as a permutation [1, 5]. We consider a group automaton A, with states 1, 2, : : : , n. The state 1 is the initial state; the set of final states is denoted by F , the alphabet by a, b, : : : , and the transitions by q 2 = ffi(q 1 ; a) or equivalently (q 1 ; a; q 2 ). 1 2 3 4 start a a b a b b a,b Figure 1. a group automaton Let us recall that two states q 1 and q 2 of an automaton are equivalent, notationally q 1 q 2 , if for every word u, the state ffi(q 1 ; u) belongs to F if and only if ffi(q 2 ; u) belongs to F . ...

Abstract not found