Timing diagrams are popular in hardware design. They have been formalized for use in reasoning tasks, such as computer-aided verification. These efforts have largely treated timing diagrams as interfaces to established notations for which verification is decidable; this has restricted timing diagrams to expressing only regular language properties. This paper presents a timing diagram logic capable of expressing certain context-free and context-sensitive properties. It shows that verification is decidable for properties expressible in this logic. More specifically, it shows that containment (...) of -regular languages generated by Büchi automata in timing diagram languages is decidable. The result relies on a correlation between timing diagram and reversal bounded counter machine languages. (shrink)

In the first part of this paper, two arguments, one by Chomsky, and one by Bar-Hillel and Shamir, are examined in detail and rejected. Both arguments purport to show that the structure of English precludes its having a finite state grammar which correctly enumerates just the well formed sentences of English. In the latter part of the paper I consider the problem of supporting claims about the structure and properties of a natural language when no grammar for the language has (...) yet been accepted. (shrink)

Mathematicians and physical scientists depend heavily on the formal symbolism of mathematics in order to express and develop their theories. For this and other reasons the last hundred years has seen a growing interest in the nature of formal language and the way it expresses meaning; particularly the objective, shared aspect of meaning as opposed to subjective, personal aspects. This dichotomy suggests the question: do the objective philosophical theories of meaning offer concepts which can be applied in psychological theories of (...) meaning? In recent years cognitive scientists such as Chomsky [1980], Fodor [1981] and MacNamara [1982] have used philosophical approaches to the meaning of formal language expressions as the basis for their psychological theories. Following this lead it seems appropriate to review some of the main treatments of meaning with a view to their transferability. (shrink)