In this paper we launch a systematic study of a subclass of ∞-regular languages called incomplete generating languages. These languages represent a non-deterministic output of a computer with finite operational memory, where the decisions are made by observing previous k states. Key-Words: Incomplete generating language, Finite automaton, Regular language.

Parikh’s theorem states that every Context Free Language (CFL) has the same Parikh image as that of a regular language. A finite state automaton accepting such a regular language is called a Parikh-equivalent automaton. In the worst case, the number of states in any non-deterministic Parikh-equivalent automaton is exponentially large in the size of the Context Free Grammar (CFG). We associate a...

Hereditarily finite (HF) set theory provides a standard universe of sets, but with no infinite sets. Its utility is demonstrated through a formalisation of the theory of regular languages and finite automata, including the Myhill-Nerode theorem and Brzozowski’s minimisation algorithm. The states of an automaton are HF sets, possibly constructed by product, sum, powerset and similar operations.

GP (for Graph Programs) is a rule-based, nondeterministic programming language for solving graph problems at a high level of abstraction, freeing programmers from dealing with low-level data structures. In this case study, we present a graph program which minimizes finite automata. The program represents an automaton by its transition diagram, computes the state equivalence relation, and merges...

Timed automata are governed by an idealized semantics that assumes a perfectly precise behavior of the clocks. The traditional semantics is not robust because the slightest perturbation in the timing of actions may lead to completely different behaviors of the automaton. Following several recent works, we consider a relaxation of this semantics, in which guards on transitions are widened by > 0...

We consider the problem of learning an unknown context-free grammar when the only knowledge available and of interest to the learner is about its structural descriptions with depth at most l. The goal is to learn a cover context-free grammar (CCFG) with respect to l, that is, a CFG whose structural descriptions with depth at most l agree with those of the unknown CFG. We propose an algorithm, c...

ion An abstract version of a program is a “simplification” of the program, with less “detail”. As such, it over-approximates the behavior of the program. The point of abstraction is to simplify the verification, by obtaining a simpler program from which we can draw conclusions about the original system [CC77, Sif84, CGL92, LGS95, KP00]. Many techniques based on abstraction compute an over-appro...

Finite state automata (FSA) are ubiquitous in computer science. Two of the most important algorithms for FSA processing are the conversion of a non-deterministic finite automaton (NFA) to a deterministic finite automaton (DFA), and then the production of the unique minimal DFA for the original NFA. We exhibit a parallel disk-based algorithm that uses a cluster of 29 commodity computers to produ...