On Varieties of Ordered Automata

The Eilenberg correspondence relates varieties of regular languages to pseudovarieties of finite monoids. Various modifications of this correspondence have been found with more general classes of regular languages on one hand and classes of more complex algebraic structures on the other hand. It is also possible to consider classes of automata instead of algebraic structures as a natural counterpart of classes of languages. Here we deal with the correspondence relating positive $\mathcal C$-varieties of languages to positive $\mathcal C$-varieties of ordered automata and we present various specific instances of this correspondence. These bring certain well-known results from a new perspective and also some new observations. Moreover, complexity aspects of the membership problem are discussed both in the particular examples and in a general setting

On Second-Order Monadic Monoidal and Groupoidal Quantifiers

We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a computational classification of the expressive power of these logics over strings with varying built-in predicates. In particular, we show that ATIME(n) can be logically characterized in terms of second-order monadic monoidal quantifiers

Inexpressibility Results for Regular Languages in Nonregular Settings

My ostensible purpose in this talk is to describe some new results (found in collaboration with Amitabha Roy) on expressibility of regular languages in certain generalizations of first-order logic. [10]. This provides me with a good excuse for describing some the work on the algebraic theory of regular languages in what one might call “nonregular settings”. The syntactic monoid and syntactic morphism of a regular language provide a highly effective tool for proving that a given regular language is not expressible or recognizable in certain compuational models, as long as the model is guaranteed to produce only regular languages. This includes finite automata, of course. but also formulas of propositional temporal logic, and first-order logic, provided one is careful to restrict the expressive power of such logics. (For example, by only allowing the order relation in first-order formulas.) Things become much harder, and quite a bit more interesting, when we drop this kind of restriction on the model. The questions that arise are important (particularly in computational complexity), and most of them are unsolved. They all point to a rich theory that extends the reach of algebraic methods beyond the domain of finite automata 1 Uniformizing Nonuniform Automata with Ramsey’s Theorem Let’s start with an especially trivial application of the syntactic monoid: Let Σ = {0, 1}, and consider the two language

Nesting Until and Since in Linear Temporal Logic

We provide an effective characterization of the "until-since hierarchy" of linear temporal logic, that is, we show how to compute for a given temporal property the minimal nesting depth in "until" and "since" required to express it. This settles the most prominent classification problem for linear temporal logic. Our characterization of the individual levels of the "until-since hierarchy" is algebraic: for each n, we present a decidable class of finite semigroups and show that a temporal property is expressible with nesting depth at most n if and only if the syntactic semigroup of the formal language associated with the property belongs to the class provided. The core of our algebraic characterization is a new description of substitution in linear temporal logic in terms of block products of finite semigroups

Entwicklung einer hierarchisch strukturierten, nichtlinearen Systementkopplung und Regelung fuer Industrieroboter

SIGLETIB Hannover: RN 8583(1988,1) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman