Related papers: On all things star-free

We study the class of star-free languages. A long-standing goal is to classify them by the complexity of their descriptions. The most influential research effort involves concatenation hierarchies, which measure alternations between…

We prove that bounded conciseness is a closed property in the space of marked groups. As a consequence, we reformulate a conjecture of Fern\'andez-Alcober and Shumyatsky [7] about conciseness in the class of residually finite groups.

The model of asynchronous programming arises in many contexts, from low-level systems software to high-level web programming. We take a language-theoretic perspective and show general decidability and undecidability results for asynchronous…

An open problem posed by Milner asks for a proof that a certain axiomatisation, which Milner showed is sound with respect to bisimilarity for regular expressions, is also complete. One of the main difficulties of the problem is the lack of…

We study the decidability of termination for two CHR dialects which, similarly to the Datalog like languages, are defined by using a signature which does not allow function symbols (of arity >0). Both languages allow the use of the =…

We show that the class of groups with $k$-multiple context-free word problem is closed under graphs of groups with finite edge groups.

We study the problem of completely automatically verifying uninterpreted programs---programs that work over arbitrary data models that provide an interpretation for the constants, functions and relations the program uses. The verification…

The purpose of this paper is to provide efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known. We develop new forbidden-chain…

We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…

An expansive, monotone operator is dominating; if it is also idempotent it is a closure operator. Although they have distinct properties, these two kinds of discrete operators are also intertwined. Every closure operator is dominating;…

The use of monoids in the study of word languages recognized by finite-state automata has been quite fruitful. In this work, we look at the same idea of "recognizability by finite monoids" for other monoids. In particular, we attempt to…

Adapting a proof of Bouscaren and Delon, we show that every type-definable connected group in a given stable theory of fields embeds into an algebraic group, under a condition on the definable closure. We also present general hypotheses…

Under certain conditions, we obtain sharp bounds on some functionals defined in the coefficient space of starlike functions. It has been found that the functionals are closely associated with certain coefficient problems, which are of…

Without prior knowledge, distinguishing different languages may be a hard task, especially when their borders are permeable. We develop an extension of spectral clustering -- a powerful unsupervised classification toolbox -- that is shown…

We show that for any class of Boolean algebras with an associative operator, if it contains the complex algebra of (P(N), U), its equational theory is undecidable. Equivalently, any associative normal modal logic valid over the frame (P(N),…

We give a new proof of quantifier elimination in the theory of all ordered abelian groups in a suitable language. More precisely, this is only "quantifier elimination relative to ordered sets" in the following sense. Each definable set in…

There are many different semantics for general logic programs (i.e. programs that use negation in the bodies of clauses). Most of these semantics are Turing complete (in a sense that can be made precise), implying that they are undecidable.…

A notion of support for objects in any Grothendieck category is introduced. This is based on the spectral category of a Grothendieck category and uses its Boolean lattice of localising subcategories. The support provides a classification of…

One of the most interesting questions concerning hierarchical control of discrete-event systems with partial observations is a condition under which the language observability is preserved between the original and the abstracted plant.…

Concatenation hierarchies are classifications of regular languages. All such hierarchies are built through the same construction process: start from an initial class of languages and build new levels using two generic operations.…