A Note on Limited Pushdown Alphabets in Stateless Deterministic Pushdown Automata

Recently, an infinite hierarchy of languages accepted by stateless deterministic pushdown automata has been established based on the number of pushdown symbols. However, the witness language for the n-th level of the hierarchy is over an input alphabet with 2(n-1) elements. In this paper, we improve this result by showing that a binary alphabet is sufficient to establish this hierarchy. As a consequence of our construction, we solve the open problem formulated by Meduna et al. Then we extend these results to m-state realtime deterministic pushdown automata, for all m at least 1. The existence of such a hierarchy for m-state deterministic pushdown automata is left open

Clearing Restarting Automata

Restartovací automaty byly navrženy jako model pro redukční analýzu, která představuje lingvisticky motivovanou metodu pro kontrolu korektnosti věty. Cílem práce je studovat omezenější modely restartovacích automatů, které smí vymazat podřetězec nebo jej nahradit speciálním pomocným symbolem, jenom na základě omezeného lokálního kontextu tohoto podřetězce. Tyto restartovací automaty se nazývají clearing restarting automata. V práci jsou taktéž zkoumány uzávěrové vlastnosti těchto automatů, jejich vztah k Chomskeho hierarchii a možnosti učení těchto automatů na základě pozitivních a negativních příkladů.Restarting automata were introduced as a model for analysis by reduction which is a linguistically motivated method for checking correctness of a sentence. The goal of the thesis is to study more restricted models of restarting automata which based on a limited context can either delete a substring of the current content of its tape or replace a substring by a special symbol, which cannot be overwritten anymore, but it can be deleted later. Such restarting automata are called clearing restarting automata. The thesis investigates the properties of clearing restarting automata, their relation to Chomsky hierarchy and possibilities for machine learning of such automata from positive and negative samples.Department of Software and Computer Science EducationKatedra softwaru a výuky informatikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Programming Languages and Systems

This open access book constitutes the proceedings of the 30th European Symposium on Programming, ESOP 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 24 papers included in this volume were carefully reviewed and selected from 79 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

The word problem and combinatorial methods for groups and semigroups

The subject matter of this thesis is combinatorial semigroup theory. It includes material, in no particular order, from combinatorial and geometric group theory, formal language theory, theoretical computer science, the history of mathematics, formal logic, model theory, graph theory, and decidability theory. In Chapter 1, we will give an overview of the mathematical background required to state the results of the remaining chapters. The only originality therein lies in the exposition of special monoids presented in §1.3, which uni.es the approaches by several authors. In Chapter 2, we introduce some general algebraic and language-theoretic constructions which will be useful in subsequent chapters. As a corollary of these general methods, we recover and generalise a recent result by Brough, Cain & Pfei.er that the class of monoids with context-free word problem is closed under taking free products. In Chapter 3, we study language-theoretic and algebraic properties of special monoids, and completely classify this theory in terms of the group of units. As a result, we generalise the Muller-Schupp theorem to special monoids, and answer a question posed by Zhang in 1992. In Chapter 4, we give a similar treatment to weakly compressible monoids, and characterise their language-theoretic properties. As a corollary, we deduce many new results for one-relation monoids, including solving the rational subset membership problem for many such monoids. We also prove, among many other results, that it is decidable whether a one-relation monoid containing a non-trivial idempotent has context-free word problem. In Chapter 5, we study context-free graphs, and connect the algebraic theory of special monoids with the geometric behaviour of their Cayley graphs. This generalises the geometric aspects of the Muller-Schupp theorem for groups to special monoids. We study the growth rate of special monoids, and prove that a special monoid of intermediate growth is a group