We give a finitary axiomatization of the algebra of regular events involving only equations and equational implications. Unlike Salomaa 's axiomatizations, the axiomatization given here is sound for all interpretations over Kleene algebras. 1 Introduction Kleene algebras are algebraic structures with operators +, \Delta, , 0, and 1 satisfying certain axioms. They arise in various guises in a number of settings: relational algebra [22, 23], semantics and logics of programs [14, 24], automata and formal language theory [18, 19], and the design and analysis of algorithms [1, 21, 12]. An important example of a Kleene algebra is Reg \Sigma , the family of regular sets over a finite alphabet \Sigma. The equational theory of this structure has been called the algebra of regular events. This theory was first studied by Infor. and Comput. 110:2 (May 1994), 366--390. A preliminary version of this paper appeared as [16]. Kleene [13], who posed axiomatization as an open problem. Salomaa [2...

This paper deals with finite size networks which consist of interconnections of synchronously evolving processors. Each processor updates its state by applying a "sigmoidal" function to a linear combination of the previous states of all units. We prove that one may simulate all Turing Machines by such nets. In particular, one can simulate any multi-stack Turing Machine in real time, and there is a net made up of 886 processors which computes a universal partial-recursive function. Products (high order nets) are not required, contrary to what had been stated in the literature. Non-deterministic Turing Machines can be simulated by non-deterministic rational nets, also in real time. The simulation result has many consequences regarding the decidability, or more generally the complexity, of questions about recursive nets.

Hybrid learning methods use theoretical knowledge of a domain and a set of classified examples to develop a method for accurately classifying examples not seen during training. The challenge of hybrid learning systems is to use the information provided by one source of information to offset information missing from the other source. By so doing, a hybrid learning system should learn more effectively than systems that use only one of the information sources. KBANN(Knowledge-Based Artificial Neural Networks) is a hybrid learning system built on top of connectionist learning techniques. It maps problem-specific "domain theories", represented in propositional logic, into neural networks and then refines this reformulated knowledge using backpropagation. KBANN is evaluated by extensive empirical tests on two problems from molecular biology. Among other results, these tests show that the networks created by KBANN generalize better than a wide variety of learning systems, as well as several t...

Abstract. We investigate conditions under which a given Kleene algebra with tests is isomorphic to an algebra of binary relations. Two simple separation properties are identified that, along with star-continuity, are sufficient for nonstandard relational representation. An algebraic condition is identified that is necessary and sufficient for the construction to produce a standard representation. 1

In this paper we define timed regular expressions, an extension of regular expressions for specifying sets of densetime discrete-valued signals. We show that this formalism is equivalent in expressive power to the timed automata of Alur and Dill by providing a translation procedure from expressions to automata and vice versa. The result is extended to !-regular expressions (B uchi's theorem). 1. Introduction Timed automata, i.e. automata equipped with clocks [AD94], have been studied extensively in recent years as they provide a rigorous model for reasoning about the quantitative temporal aspects of systems. Together with realtime logics and process algebras they constitute the underlying theoretical basis for the specification and verification of real-time systems. Kleene's theorem [K56], stating that the regular (or rational) subsets of \Sigma are exactly the recognizable ones (those accepted by finite automata), is one of the cornerstones of automata theory. No such theorem has ...

We define general algebraic frameworks for shortest-distance problems based on the structure of semirings. We give a generic algorithm for finding single-source shortest distances in a weighted directed graph when the weights satisfy the conditions of our general semiring framework. The same algorithm can be used to solve efficiently classical shortest paths problems or to find the k-shortest distances in a directed graph. It can be used to solve single-source shortest-distance problems in weighted directed acyclic graphs over any semiring. We examine several semirings and describe some specific instances of our generic algorithms to illustrate their use and compare them with existing methods and algorithms. The proof of the soundness of all algorithms is given in detail, including their pseudocode and a full analysis of their running time complexity.

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 present treatment of automata theory may serve as an introduction to coalgebra.

Current dynamic epistemic logics often become cumbersome and opaque when common knowledge is added for groups of agents. Still, postconditions regarding common knowledge express the essence of what communication achieves. We propose new systems that extend the underlying static epistemic languages in such a way that completeness proofs for the full dynamic systems can be obtained by perspicuous reduction axioms. Also, we include factual alteration, rather than just information change, which allows us to cover a much wider range of phenomena in the area of communication and change. 1

The timed automaton model of [LV92, LV93] is a general model for timing-based systems. A notion of timed action transducer is here defined as an automata-theoretic way of representing operations on timed automata. It is shown that two timed trace inclusion relations are substitutive with respect to operations that can be described by timed action transducers. Examples are given of operations that can be described in this way, and a preliminary proposal is given for an appropriate language of operators for describing timing-based systems.

A logic simulator can prove the correctness of a digital circuit if it can be shown that only circuits fulfilling the system specification will produce a particular response to a sequence of simulation commands. This style of verification has advantages over other proof methods in being readily automated and requiring less attention on the part of the user to the low-level details of the design. It has advantages over other approaches to simulation in providing more reliable results, often at a comparable cost.