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Every semigroup which is a finite disjoint union of copies of the free mono- genic semigroup (natural numbers under addition) has soluble word prob- lem and soluble membership problem. Efficient algorithms are given for both problems.
The theory of finite automata concerns itself with words in a free monoid together with concatenation and without further structure. There are, however, important applications which use alphabets which are structured in some sense. We…
We study the links between the topological complexity of an omega context free language and its degree of ambiguity. In particular, using known facts from classical descriptive set theory, we prove that non Borel omega context free…
We prove that a group has word problem that is a growing context-sensitive language precisely if its word problem can be solved using a non-deterministic Cannon's algorithm (the deterministic algorithms being defined by Goodman and…
ADOMIT is an algorithm for Automatic Detection of OMIssions in Translations. The algorithm relies solely on geometric analysis of bitext maps and uses no linguistic information. This property allows it to deal equally well with omissions…
We show a new and constructive proof of the following language-theoretic result: for every context-free language L, there is a bounded context-free language L' included in L which has the same Parikh (commutative) image as L. Bounded…
Motivated by a historical combinatorial problem that resembles the well-known Josephus problem, we investigate circular partition algorithms and formulate problems in deterministic finite automata with practical algorithms. The historical…
Constraint Satisfaction Problem on finite sets is known to be NP-complete in general but certain restrictions on the constraint language can ensure tractability. It was proved that if a constraint language has a weak near unanimity…
A regular language $L$ is union-free if it can be represented by a regular expression without the union operation. A union-free language is deterministic if it can be accepted by a deterministic one-cycle-free-path finite automaton; this is…
We provide an algorithm for deciding simple grammar bisimilarity whose complexity is polynomial in the valuation of the grammar (maximum seminorm among production rules). Since the valuation is at most exponential in the size of the…
We consider the fair allocation of indivisible items to several agents with additional conflict constraints. These are represented by a conflict graph where each item corresponds to a vertex of the graph and edges in the graph represent…
We define the problem of learning a transducer ${S}$ from a target language $U$ containing possibly conflicting transducers, using membership queries and conjecture queries. The requirement is that the language of ${S}$ be a subset of $U$.…
Let $F_n$ be the free group of a finite rank $n$. We study orbits $Orb_{\phi}(u)$, where $u$ is an element of the group $F_n$, under the action of an automorphism $\phi$. If an orbit like that is finite, we determine precisely what its…
An attractive mechanism to specify global constraints in rostering and other domains is via formal languages. For instance, the Regular and Grammar constraints specify constraints in terms of the languages accepted by an automaton and a…
Consider $ A^* $, the free monoid generated by the finite alphabet $A$ with the concatenation operation. Two words have the same commutative image when one is a permutation of the symbols of the other. The commutative closure of a set $ L…
We characterize the meaning of words with language-independent numerical fingerprints, through a mathematical analysis of recurring patterns in texts. Approximating texts by Markov processes on a long-range time scale, we are able to…
We describe a practical algorithm for computing normal forms for semigroups and monoids with finite presentations satisfying so-called small overlap conditions. Small overlap conditions are natural conditions on the relations in a…
We consider some questions about formal languages that arise when inverses of letters, words and languages are defined. The reduced representation of a language over the free monoid is its unique equivalent representation in the free group.…
We introduce layered automata, a subclass of alternating parity automata that generalises deterministic automata. Assuming a consistency property, these automata are history deterministic and 0-1 probabilistic. We show that every…
With each semigroup one can associate a partial algebra, called the biordered set, which captures important algebraic and geometric features of the structure of idempotents of that semigroup. For a biordered set $\mathcal{E}$, one can…