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There are several finite axiomatizations of stratified comprehension. The famous two are Hailperin's and Randall Holmes's. However, the system presented here could be the shortest known one written in the first order language of set theory.…

Saturation is a fundamental game-semantic property satisfied by strategies that interpret higher-order concurrent programs. It states that the strategy must be closed under certain rearrangements of moves, and corresponds to the intuition…

These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…

A generalized set theory (GST) is like a standard set theory but also can have non-set structured objects that can contain other structured objects including sets. This paper presents Isabelle/HOL support for GSTs, which are treated as type…

While many applications of automata in formal methods can use nondeterministic automata, some applications, most notably synthesis, need deterministic or good-for-games (GFG) automata. The latter are nondeterministic automata that can…

This paper provides a description of the algorithms employed by the Warwick AUTOMATA package for calculating the finite state automata associated with a short-lex automatic group. The aim is to provide an overview of the whole process,…

An automatic sequence is a letter-to-letter coding of a fixed point of a uniform morphism. More generally, we have morphic sequences, which are letter-to-letter codings of fixed points of arbitrary morphisms. There are many examples where…

We propose a new symbolic trace semantics for register automata (extended finite state machines) which records both the sequence of input symbols that occur during a run as well as the constraints on input parameters that are imposed by…

Nominal sets provide a foundation for reasoning about names. They are used primarily in syntax with binders, but also, e.g., to model automata over infinite alphabets. In this paper, nominal sets are related to nominal renaming sets, which…

Several methods are discussed that construct a finite automaton given a context-free grammar, including both methods that lead to subsets and those that lead to supersets of the original context-free language. Some of these methods of…

We prove, for various important classes of Mealy automata, that almost all generated groups have an element of infinite order. In certain cases, it also implies other results such as exponential growth.

This paper describes an abstract machine for linguistic formalisms that are based on typed feature structures, such as HPSG. The core design of the abstract machine is given in detail, including the compilation process from a high-level…

Profinite semigroups are a generalization of finite semigroups that come about naturally when one is interested in considering free structures with respect to classes of finite semigroups. They also appear naturally through dualization of…

The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to…

We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…

We consider the structures given by repeatedly generalising the definition of finite state automata by symmetry considerations, and constructing analogues of transition monoids at each step. This approach first gives us non-deterministic…

In this work, we propose an abstraction and refinement methodology for the controller synthesis of discrete-time stochastic systems to enforce complex logical properties expressed by deterministic finite automata (a.k.a. DFA). Our proposed…

We introduce a new measure on regular languages: their nondeterministic syntactic complexity. It is the least degree of any extension of the `canonical boolean representation' of the syntactic monoid. Equivalently, it is the least number of…

Regular languages -- the languages accepted by deterministic finite automata -- are known to be precisely the languages recognized by finite monoids. This characterization is the origin of algebraic language theory. In this paper, we…

This is a tutorial on finite automata. We present the standard material on determinization and minimization, as well as an account of the equivalence of finite automata and monadic second-order logic. We conclude with an introduction to the…