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...

We follow a connection between tight determinisation and complementation and establish a complementation procedure from transition-labelled parity automata to transition-labelled nondeterministic Büchi automata. We prove it to be tight up to an O(n) factor, where n is the size of the nondeterministic parity automaton. This factor does not depend on the number of priorities.

I was supposed to deliver one of the speeches at Wolfgang Thomas’s retirement ceremony. Wolfgang had called me on the phone earlier and posed some questions about temporal logic, but I hadn’t had good answers at the time. What I decided to do at the ceremony was to take up the conversation again and show how it could have evolved if only I had put more effort into answering his questions. Here ...

This paper reports extensions to the GOAL tool that enable it to become a research tool for omega automata and temporal logic. The extensions include an expanded collection of translation, simplification, and complementation algorithms, a command-line mode which makes GOAL functions accessible by programs, and utility functions for such common tasks as file format conversion, random formulae ge...

background: to assess the effect of supplementation with vitamins a, e and c and ω-3 fatty acids on lipid peroxidation in strepto zotocin (stz) induced diabetic rats. methods: sixty four male wistar rats weighting 250g were divided into four groups as normal control, diabetic control, dia betic with vitamin a, e as well as c supplementation and diabetic with ω-3 fatty acids supplementation. aft...

Brooks’ Theorem implies that if a graph has ∆ ≥ 3 and and χ > ∆, then ω = ∆+1. Borodin and Kostochka conjectured that if ∆ ≥ 9 and χ ≥ ∆, then ω ≥ ∆. We show that if ∆ ≥ 13 and χ ≥ ∆, then ω ≥ ∆ − 3. For a graph G, let H(G) denote the subgraph of G induced by vertices of degree ∆. We also show that if χ ≥ ∆, then ω ≥ ∆ or ω(H(G)) ≥ ∆− 5.

A new, self-contained, proof of a coherence result for categories equipped with two symmetric monoidal structures bridged by a natural transformation is given. It is shown that this coherence result is sufficient for ω×ω-indexed family of iterated reduced bar constructions based on such a category. Mathematics Subject Classification (2000): 18D10, 55P47

An ideal I over Pκλ is said to be σ-strategically closed, proper or semiproper if the corresponding poset PI is σ-strategically closed, proper or semiproper, respectively. In this note we prove the following: • If there exists a σ-strategically closed, fine and κ-complete ideal over Pω2λ for some λ ≥ ω2 then ♦ω1 holds. • If there exists a proper, fine and κ-complete ideal over Pω2λ for some λ ≥...