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2 results

  • COMPLEXITY OF THE INFINITARY LAMBEK CALCULUS WITH KLEENE STAR

  • Part of
  • STEPAN KUZNETSOV
  • Journal:
    The Review of Symbolic Logic / Volume 14 / Issue 4 / December 2021
    Published online by Cambridge University Press:
    22 July 2020, pp. 946-972
    Print publication:
    December 2021

  • We consider the Lambek calculus, or noncommutative multiplicative intuitionistic linear logic, extended with iteration, or Kleene star, axiomatised by means of an $\omega $ -rule, and prove that the derivability problem in this calculus is $\Pi _1^0$ -hard. This solves a problem left open by Buszkowski (2007), who obtained the same complexity bound for infinitary action logic, which additionally includes additive conjunction and disjunction. As a by-product, we prove that any context-free language without the empty word can be generated by a Lambek grammar with unique type assignment, without Lambek’s nonemptiness restriction imposed (cf. Safiullin, 2007).

  • 1 - Formal Preliminaries

  • from Part I - Formal Background
  • Stoyan Mihov, Klaus U. Schulz, Ludwig-Maximilians-Universität Munchen
  • Book:
    Finite-State Techniques
    Published online:
    29 July 2019
    Print publication:
    01 August 2019, pp 3-22

  • Summary

    The aim of this chapter is twofold. First, we recall a collection of basic mathematical notions that are needed for the discussions of the following chapters. Second, we have a first, still purely mathematical, look at the central topics of the book: languages, relations and functions between strings, as well as important operations on languages, relations and functions. We also introduce monoids, a class of algebraic structures that gives an abstract view on strings, languages, and relations.