Related papers: Closing star-free closure
We examine the complexity of basic regular operations on languages represented by Boolean and alternating finite automata. We get tight upper bounds m+n and m+n+1 for union, intersection, and difference, 2^m+n and 2^m+n+1 for concatenation,…
The main theorem provides a characterisation of the finite rank operators lying in a norm closed Lie ideal of a continuous nest algebra. These operators are charaterised as those finite rank operators in the nest algebra satisfying a…
We give another proof of a theorem of Fife - understood broadly as providing a finite automaton that gives a complete description of all infinite binary overlap-free words. Our proof is significantly simpler than those in the literature. As…
We introduce a high-level language with Python-like syntax for string-to-string, polyregular, first-order definable transductions. This language features function calls, boolean variables, and nested for-loops. We devise and implement a…
We present a fixed point theorem for a class of (potentially) non-monotonic functions over specially structured complete lattices. The theorem has as a special case the Knaster-Tarski fixed point theorem when restricted to the case of…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
Automatic structures are first-order structures whose universe and relations can be represented as regular languages. It follows from the standard closure properties of regular languages that the first-order theory of an automatic structure…
We study the state complexity of boolean operations, concatenation and star with one or two of the argument languages reversed. We derive tight upper bounds for the symmetric differences and differences of such languages. We prove that the…
Context-free language theory is a well-established area of mathematics, relevant to computer science foundations and technology. This paper presents the preliminary results of an ongoing formalization project using context-free grammars and…
We present a trichotomy theorem for the quantum query complexity of regular languages. Every regular language has quantum query complexity Theta(1), ~Theta(sqrt n), or Theta(n). The extreme uniformity of regular languages prevents them from…
Kleene algebra axioms are complete with respect to both language models and binary relation models. In particular, two regular expressions recognise the same language if and only if they are universally equivalent in the model of binary…
The tractability of certain CSPs for dense or sparse instances is known from the 90s. Recently, the densification and the sparsification of CSPs were formulated as computational tasks and the systematical study of their computational…
Humans can classify data of an unseen category by reasoning on its language explanations. This ability is owing to the compositional nature of language: we can combine previously seen attributes to describe the new category. For example, we…
We study the problem of disentangling locked processes via code refactoring. We identify and characterise a class of processes that is not lock-free; then we formalise an algorithm that statically detects potential locks and propose…
We consider closure properties in the class of positively decreasing distributions. Our results stem from different types of dependence, but each type belongs in the family of asymptotically independent dependence structure. Namely we…
We prove two completeness results for Kleene algebra with tests and a top element, with respect to guarded string languages and binary relations. While the equational theories of those two classes of models coincide over the signature of…
Termination of logic programs depends critically on the selection rule, i.e. the rule that determines which atom is selected in each resolution step. In this article, we classify programs (and queries) according to the selection rules for…
Stop words, which are considered non-predictive, are often eliminated in natural language processing tasks. However, the definition of uninformative vocabulary is vague, so most algorithms use general knowledge-based stop lists to remove…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
For a class L of languages let PDL[L] be an extension of Propositional Dynamic Logic which allows programs to be in a language of L rather than just to be regular. If L contains a non-regular language, PDL[L] can express non-regular…