Eco-colonies are new grammar systems with very simple grammars called agents placed in a common dynamic environment. Every agent generates its own finite language, all agents cooperate on the shared environment. The environment is developing not only by the action of agents, but also using its own developmental rules. The generative power of eco-colonies was discussed in several papers, ecocolo...

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 and Davies characterized the regular languages meeting these bounds. To achieve these results, they used the so-called “átomaton” of a language, introduced by Brz...

Geometrical languages generalize languages introduced to model temporal validation of real-time softwares. We prove that it is decidable whether a regular language is geometrical. This result was previously known for binary languages.

In the paper, we continue our study on state complexity of combined operations. We study the state complexities of L1 ∪ L2, k ∪ i=1 Li , L ∗ 1 ∩ L2, and k ∩ i=1 Li for regular languages Li, 1 ≤ i ≤ k. We obtain the exact bounds for these combined operations and show that the bounds are different from the mathematical compositions of the state complexities of their component individual operations.

advance a modern extension formation of cubic vague sets identified as interval (CIVSs). similarly describe the idea (ICIVSs) (ECIVSs) by examples debate their exciting properties, excluding ICIVSs ECIVSs - . Additionally, show ( ECIVSs) necessity not be an ICIVS (or ECIVS). apply (CIVS) to topological spaces and present spaces. Further, we introduce P-cubic space R-cubic space. We discuss basi...

We initiate a study of languages of partial words related to regular languages of full words. First, we investigate the possibility of expressing a regular language of full words as the image of a partial-words-language through a substitution that only replaces the hole symbols of the partial words by a finite set of letters. Results regarding the structure, uniqueness and succinctness of such ...

In this note, we give a construction that provides a tight lower bound of mn − 1 for the length of the shortest word in the intersection of two regular languages with state complexities m and n.

We develop an algebraic model for recognizing languages of words indexed by countable linear orderings. This notion of recognizability is effectively equivalent to definability in monadic second-order (MSO) logic. The proofs also imply the first known collapse result for MSO logic over countable linear orderings.

The hairpin completion is a formal operation inspired from DNA biochemistry. It is known that the (one step) hairpin completion of regular language is linear contextfree, but not regular in general. It is decidable whether the (one step) hairpin completion of regular language is regular. However, it is an open question whether the iterated hairpin completion of a regular language is regular, ev...