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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…
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.…
We study the notion of sparseness for regular languages over finite trees and infinite words. A language of trees is called sparse if the relative number of $n$-node trees in the language tends to zero, and a language of infinite words is…
We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…
We show that for any $i > 0$, it is decidable, given a regular language, whether it is expressible in the $\Sigma_i[<]$ fragment of first-order logic FO[<]. This settles a question open since 1971. Our main technical result relies on the…
Let S be a finite set of words over an alphabet Sigma. The set S is said to be complete if every word w over the alphabet Sigma is a factor of some element of S*, i.e. w belongs to Fact(S*). Otherwise if S is not complete, we are interested…
A separator for two languages is a third language containing the first one and disjoint from the second one. We investigate the following decision problem: given two regular input languages, decide whether there exists a locally testable…
A locally testable language L is a language with the property that for some non negative integer k, called the order of local testability, whether or not a word u is in the language L depends on (1) the prefix and suffix of the word u of…
We present a non-vacuous definition of compositionality. It is based on the idea of combining the minimum description length principle with the original definition of compositionality (that is, that the meaning of the whole is a function of…
Foundations of formal languages, as subfield of theoretical computer science, are part of typical upper secondary education curricula. There is very little research on the potential difficulties that students at this level have with this…
A language $L$ is said to be dense if every word in the universe is an infix of some word in $L$. This notion has been generalized from the infix operation to arbitrary word operations $\varrho$ in place of the infix operation…
The article continues the study of the genus of regular languages that the authors introduced in a 2012 paper. Generalizing a previous result, we produce a new family of regular languages on a two-letter alphabet having arbitrary high…
Given an infinite linear group with a finite set of generators, we show that the shortest word length of an element of infinite order has an upper bound that depends only on the number of generators and the degree. This provides a…
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…
When can two regular word languages K and L be separated by a simple language? We investigate this question and consider separation by piecewise- and suffix-testable languages and variants thereof. We give characterizations of when two…
The separability problem for word languages of a class $\mathcal{C}$ by languages of a class $\mathcal{S}$ asks, for two given languages $I$ and $E$ from $\mathcal{C}$, whether there exists a language $S$ from $\mathcal{S}$ that includes…
Recently, it was shown that any theory of strings containing the string-replace function (even the most restricted version where pattern/replacement strings are both constant strings) becomes undecidable if we do not impose some kind of…
For some fixed alphabet A, a language L of A* is in the class L(1/2) of the Straubing-Therien hierarchy if and only if it can be expressed as a finite union of languages A*aA*bA*...A*cA*, where a,b,...,c are letters. The class L(1) is…
We study the following rearrangement problem: Given $n$ words, rearrange and concatenate them so that the obtained string is lexicographically smallest (or largest, respectively). We show that this problem reduces to sorting the given words…
Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. Length constraints restrict valid substitutions of…