Terminating left-hand sides of scattered context productions M. Nivat

AbstractThe left-hand side of a scattered context production, (A1,A2,…,An)→(x1,x2,…,xn), is terminating if A1A2…An derives a terminal word. This paper discusses scattered context grammars whose sentential forms contain sequences of nonterminals formed by shuffling the terminating left-hand sides of productions. It proves that these grammars do not generate some context-sensitive languages, so they are less powerful than the scattered context grammars whose sentential forms are unrestricted. In its conclusion, this paper demonstrates the impact of this result and discusses open problems

Regulated Formal Models and Their Reduction

Department of Theoretical Computer Science and Mathematical LogicKatedra teoretické informatiky a matematické logikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Mechanised Uniform Interpolation for Modal Logics K, GL, and iSL

The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal logics, namely: (1) the modal logic K, for which a pen-and-paper proof exists; (2) Gödel-Löb logic GL, for which our formalisation clarifies an important point in an existing, but incomplete, sequent-style proof; and (3) intuitionistic strong Löb logic iSL, for which this is the first proof-theoretic construction of uniform interpolants. Our work also yields verified programs that allow one to compute the propositional quantifiers on any formula in this logic

Mechanised Uniform Interpolation for Modal Logics K, GL, and iSL

The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal logics, namely: (1) the modal logic K, for which a pen-and-paper proof exists; (2) Gödel-Löb logic GL, for which our formalisation clarifies an important point in an existing, but incomplete, sequent-style proof; and (3) intuitionistic strong Löb logic iSL, for which this is the first proof-theoretic construction of uniform interpolants. Our work also yields verified programs that allow one to compute the propositional quantifiers on any formula in this logic

Andrey Bely: A Critical Review

Andrey Bely, novelist, essayist, theoretician, critic, and poet, was a central figure in the Russian Symbolist movement of the 1920s, the most important literary movement in Russia in this century. Bely articulated a Symbolist aesthetic and originated a new approach to the study of Russian metrics and versification, giving rise to a new scholarly discipline that still thrives in the West. Although regarded by some critics, including Vladimir Nabokov, as the author of the greatest Russian novel of this century, Bely has been nearly forgotten in his native country for ideological reasons. In the West he remains little known and generally under-valued. But with recent English translations of Kotik Letaev and his masterpiece, Petersburg, interest in Bely is increasing. Janecek\u27s book brings together some of the best modern scholarship on Bely and the Russian Symbolist movement of the 1920s. Gerald Janecek is associate professor of Russian at the University of Kentucky.https://uknowledge.uky.edu/upk_slavic_languages_and_societies/1001/thumbnail.jp

Rational monoid and semigroup automata

We consider a natural extension to the definition of M-automata which allows the automaton to make use of more of the structure of the monoid M, and by removing the reliance on an identity element, allows the definition of S-automata for S an arbitrary semigroup. In the case of monoids, the resulting automata are equivalent to valence automata with rational target sets which arise in the theory of regulated rewriting. We focus on the polycyclic monoids, and show that for polycyclic monoids of rank 2 or more they accept precisely the context-free languages. The case of the bicyclic monoid is also considered. In the process we prove a number of interesting results about rational subsets in polycyclic monoids; as a consequence we prove the decidability of the rational subset membership problem, and the closure of the class of rational subsets under intersection and complement. In the case of semigroups, we consider the important class of completely simple and completely 0-simple semigroups, obtaining a complete characterisation of the classes of languages corresponding to such semigroups, in terms of their maximal subgroups. In the process, we obtain a number of interesting results about rational subsets of Rees matrix semigroups.EThOS - Electronic Theses Online ServiceGBUnited Kingdo