In an earlier paper, the author used derivatives to construct a deterministic automaton recognizing the language defined by an ω-regular expression. The construction was related to a determinization method invented by Safra. This paper describes a new construction, inspired by Piterman’s improvement to Safra’s method. It produces an automaton with fewer states. In addition, the presentation and...

The complementation problem for nondeterministic word automata has numerous applications in formal verification. In particular, the language-containment problem, to which many verification problems are reduced, involves complementation. For automata on finite words, which correspond to safety properties, complementation involves determinization. The 2 blow-up that is caused by the subset constr...

The aim of this paper is to investigate how subset construction performs on specific families of automata. A new upper bound on the number of states of the subset-automaton is established in the case of homogeneous automata. The complexity of the two basic steps of subset construction, i.e. the computation of deterministic transitions and the set equality tests, is examined depending on whether...

In this paper we regard languages and their acceptors – such as deterministic or weighted automata, transducers, or monoids – as functors from input categories that specify the type of the languages and of the machines to categories that specify the type of outputs. Our results are as follows: a) We provide sufficient conditions on the output category so that minimization of the corresponding a...

The convexity of numerical domains such as polyhedra, octagons, intervals and linear equalities enables tractable analysis of software for buffer overflows, null pointer dereferences and floating point errors. However, convexity also causes the analysis to fail in many common cases. Powerset extensions can remedy this shortcoming by considering disjunctions of predicates. Unfortunately, analysi...

In this paper, let $L$ be a completeresiduated lattice, and let {bf Set} denote the category of setsand mappings, $LF$-{bf Pos} denote the category of $LF$-posets and$LF$-monotone mappings, and $LF$-{bf CSLat}$(sqcup)$, $LF$-{bfCSLat}$(sqcap)$ denote the category of $LF$-completelattices and $LF$-join-preserving mappings and the category of$LF$-complete lattices and $LF$-meet-preserving mapping...

We give a technique to construct a final coalgebra in which each element is a set of formulas of modal logic. The technique works for both the finite and the countable powerset functors. Starting with an injectively structured, corecursive algebra, we coinductively obtain a suitable subalgebra called the “co-founded part”. We see – first with an example, and then in the general setting of modal...

It has remained an open question whether the twins property for weighted tree automata is decidable. This property is crucial for determinizing such an automaton, and it has been argued that determinization improves the output of parsers and translation systems. We show that the twins property for weighted tree automata over extremal semifields is decidable.

We study the problem of reducing the size of a language model while preserving recognition performance (accuracy and speed). A successful approach has been to represent language models by weighted nite-state automata (WFAs). Analogues of classical automata determinization and minimization algorithms then provide a general method to produce smaller but equivalent WFAs. We extend this approach by...

We examine the determinization of monitors. We demonstrate that every monitor is equivalent to a deterministic one, which is at most doubly exponential in size with respect to the original monitor. When monitors are described as CCS-like processes, this doubly-exponential bound is optimal. When (deterministic) monitors are described as finite automata (as their LTS), then they can be exponentia...