Related papers: State complexity of catenation combined with boole…
An algebraic structure with two constants and one ternary operation, which is not completely commutative, is put forward to accommodate ternary Boolean algebras. When the ternary operation is interpreted as Church's conditioned disjunction,…
According to a previous result by S. V. Avgustinovich and the author, each factorial language admits a unique canonical decomposition to a catenation of factorial languages. In this paper, we analyze the appearance of the canonical…
In this paper we define and investigate the binary word operation of strong-$\phi$-bi-catenation (denoted by $\leftrightarrows_\phi$) where $\phi$ is either a morphic or an antimorphic involution. In particular, we concentrate on the…
We present a new technique for demonstrating the reachability of states in deterministic finite automata representing the concatenation of two languages. Such demonstrations are a necessary step in establishing the state complexity of the…
We examine deterministic and nondeterministic state complexities of regular operations on prefix-free languages. We strengthen several results by providing witness languages over smaller alphabets, usually as small as possible. We next…
We resolve an open question by determining matching (asymptotic) upper and lower bounds on the state complexity of the operation that sends a language L to (c(L*))*, where c() denotes complement.
We describe witness languages meeting the upper bound on the state complexity of the multiple concatenation of $k$ regular languages over an alphabet of size $k+1$ with a significantly simpler proof than that in the literature. We also…
We study the state complexity of binary operations on regular languages over different alphabets. It is known that if $L'_m$ and $L_n$ are languages of state complexities $m$ and $n$, respectively, and restricted to the same alphabet, the…
In previous work "Betweenness algebras" we introduced and examined the class of betweenness algebras. In the current paper we study a larger class of algebras with binary operators of possibility and sufficiency, the weak mixed algebras.…
We consider the numbers arising in the problem of normal ordering of expressions in canonical boson creation and annihilation operators. We treat a general form of a boson string which is shown to be associated with generalizations of…
Atoms of a (regular) language $L$ were introduced by Brzozowski and Tamm in 2011 as intersections of complemented and uncomplemented quotients of $L$. They derived tight upper bounds on the complexity of atoms in 2013. In 2014, Brzozowski…
We examine the complexity of inference in Bayesian networks specified by logical languages. We consider representations that range from fragments of propositional logic to function-free first-order logic with equality; in doing so we cover…
Two classes of methods have been shown to be useful for resolving lexical ambiguity. The first relies on the presence of particular words within some distance of the ambiguous target word; the second uses the pattern of words and…
We present a combinatorial method of constructing solutions to the normal ordering of boson operators. Generalizations of standard combinatorial notions - the Stirling and Bell numbers, Bell polynomials and Dobinski relations - lead to…
In this tutorial, we will survey known results on the complexity of conjunctive query evaluation in different settings, ranging from Boolean queries over counting to more complex models like enumeration and direct access. A particular focus…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
We introduce and study a class of betweenness algebras-Boolean algebras with binary operators, closely related to ternary frames with a betweenness relation. From various axioms for betweenness, we chose those that are most common, which…
We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in…
Multitildes are regular operators that were introduced by Caron et al. in order to increase the number of Glushkov automata. In this paper, we study the family of the multitilde operators from an algebraic point of view using the notion of…
A celebrated 1922 theorem of Kuratowski states that there are at most 14 distinct sets arising from applying the operations of complementation and closure, any number of times, in any order, to a subset of a topological space. In this paper…