We investigate the power of first-order logic with only two variables over Ï‰-words and finite words, a logic denoted by FO. We prove that FO can express precisely the same properties as linearâ€¦ (More)

We give efficient algorithms, improving optimal known bounds, for computing a variety of simulation relations on the state space of a BÃ¼chi automaton. Our algorithms are derived via a unified andâ€¦ (More)

Biologists have used a wide range of organisms to study the origin of taxa and their subsequent evolutionary change in space and time. One commonly used tool is the molecular clock approach, relatingâ€¦ (More)

We show a property of strings is expressible in the two-variable fragment of first-order logic if and only if it is expressible by both a 2 and a 2 sentence. We thereby establish: UTL = FO2 = 2 \ 2 =â€¦ (More)

Worldwide ancient lakes have been a major focal point of geological, biological, and ecological research, and key concepts in, for example, evolutionary biology are partly based on ancient lakeâ€¦ (More)

This paper surveys recent results on the classiication of discrete temporal properties, gives an introduction to the methods that have been developed to obtain them, and explains the connections toâ€¦ (More)

A monadic second-order language, denoted by Ld, is introduced for the speciication of sets of timed state sequences. A fragment of Ld, denoted by L $ d, is proved to be expressively complete forâ€¦ (More)