Hybrid systems are interacting systems of digital automata and continuous plants subject to disturbances. The digital automata are used to force the state trajectory of the continuous plant to obey a performance specification. For the basic concepts and notation for hybrid systems, see Kohn and Nerode (1993), and other papers in the same volume. Here we introduce tools for analyzing enforcing v...

Nerode et al. [ 131 showed that a correct concurrent program can be viewed as a winning strategy in a suitably defined two player game played between the Programmer and the Computer in which the program specification is defined by the rules of the game together with the winning condition. This gives rise to the question as to whether there are useful algorithms to extract (provably) winning str...

We prove that every distributive algebraic lattice with at most א1 compact elements is isomorphic to the normal subgroup lattice of some group and to the submodule lattice of some right module. The א1 bound is optimal, as we find a distributive algebraic lattice D with א2 compact elements that is not isomorphic to the congruence lattice of any algebra with almost permutable congruences (hence n...

Congruence is the degree to which one’s personality matches one’s behavior in a particular situation. On four separate occasions over several weeks, 202 undergraduate participants described a situation they encountered the previous day and their behavior. Analyses considered overall congruence as well as distinctive congruence, adjusted for the match of personality and behavior to the normative...

he purpose of this work is to introduce and study the concept of minimal deterministic automaton with IF-outputs which realizes the given IF-language. Among two methods for construction of such automaton presented here, one is based on Myhill-Nerode's theory while the other is based on derivatives of the given IF-language. Meanwhile, the categories of deterministic automata with IF-outputs and ...

The present paper is an attempt to study the minimal BL-general fuzzy automata which realizes the given fuzzy behavior. Of two methods applied for construction of such automaton presented here, one has been based on Myhill-Nerode's theory while the other has been based on derivatives of the given fuzzy behavior. Meanwhile, the categories of BL-general fuzzy automata and fuzzy behavior, along wi...

The theory of chi processes with the mismatch operator is studied. Two open congruence relations are investigated. These are weak early open congruence and weak late open congruence. Complete systems are given for both congruence relations. These systems use some new tau laws. The results of this paper correct some popular mistakes in literature.

A lattice identity is given such that it holds but its dual fails in the normal subgroup lattices of metaabelian groups. Thus the congruence variety of metaabelian groups is not self-dual; this is the first example for a modular congruence variety which is not self-dual. For a ring R with unit element let L(R) denote the class of lattices embeddable in submodule lattices of R-modules. Then HL(R...

This paper deenes a congruence relation on Gamma programs. Based on this congruence relation, laws for transforming programs are derived. We deene an axiomatic semantics for Gamma based on Brookes' transition assertions. The deenition of the congruence is in terms of provable satissability of such assertions. We consider the relationship between our congruence and other orderings that have been...