1. Preamble: Kleene [1943], Post [1944] and Mostowski [1947] . . . . . . . . . 2 1A. Post’s degrees of unsolvability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1B. Kleene’s arithmetical hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1C. Kleene [1943] vs. Post [1944] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1D. Mostowski [1...

Many decision problems concerning cellular automata are known to be decidable in the case of algebraic automata, that is, when state set has an structure and automaton acts as a morphism. The most studied cases include finite fields, commutative rings groups. In this paper, we provide methods generalize these results broader group where is (possibly non-commutative) group. configuration space n...

This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church’s intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of ref...

In this paper we give a semantic proof of cut-elimination for ICTT. ICTT is an intuitionistic formulation of Church’s theory of types defined by Miller, Scedrov, Nadathur and Pfenning in the late 1980s. It is the basis for the λprolog programming language. Our approach, extending techniques of Takahashi, Andrews and tableaux machinery of Fitting, Smullyan, Nerode and Shore, is to prove a comple...

Call a string-to-string function regular if it can be realised by one of the following equivalent models: mso transductions, two-way deterministic automata with output, and streaming transducers with registers. This paper proposes to treat origin information as part of the semantics of a regular string-to-string function. With such semantics, the model admits a machine-independent characterisat...

Strictly Local Stringsets Membership in a Strictly 2-Local (SL2) stringset (McNaughton and Papert 1971) is determined by the initial symbol, by the pairs of symbols that occur in the string and by the final symbol (independently). Thus they can be specified by giving a set of pairs of symbols drawn from the alphabet augmented by a start and an end marker. The members of the stringset are all an...

This chapter gives an overview on what is often called the algebraic theory of finite automata. It deals with languages, automata and semigroups, and has connections with model theory in logic, boolean circuits, symbolic dynamics and topology. Kleene’s theorem [70] is usually considered as the foundation of this theory. It shows that the class of recognizable languages (i.e. recognized by finit...