Marked systems and circular splicing
Splicing systems are generative devices of formal languages, introduced by Head in 1987 to model biological phenomena on linear and circular DNA molecules. In this paper we introduce a special class of finite circular splicing systems named marked systems. We prove that a marked system S generates a regular circular language if and only if S satisfies a special (decidable) property. As a consequence, we show that we can decide whether a regular circular language is generated by a marked system and we characterize the structure of these regular circular languages.
Unavoidable sets and circular splicing languages
Circular splicing systems are a formal model of a generative mechanism of circular words, inspired by a recombinant behaviour of circular DNA. They are defined by a finite alphabet A, an initial set I of circular words, and a set R of rules. In this paper, we focus on the still unknown relations between regular languages and circular splicing systems with a finite initial set and a finite set R of rules represented by a pair of letters ( ( 1 , 3 ) -CSSH systems). When R = A × A , it is known that the set of all words corresponding to the splicing language belongs to the class of pure unitary languages, introduced by Ehrenfeucht, Haussler, Rozenberg in 1983. They also provided a characteriza…
Coding with traces
We prove that the existence of a coding between two trace monoids is decidable for some families of trace monoids. Decidability heavily depends on the structure of the dependence graphs. The concept of coding is based on the new notion of strong morphism between trace monoids.
Recent results on syntactic groups of prefix codes
International audience; We give a simplified presentation of groups in transformation monoids. We use this presentation to describe two recent results on syntactic groups of prefix codes. The first one uses Sturmian words to build finite bifix codes with a given permutation group as syntactic group. The second one describes a class of prefix codes such that all their syntactic groups are cyclic.
A characterization of regular circular languages generated by marked splicing systems
AbstractSplicing systems are generative devices of formal languages, introduced by Head in 1987 to model biological phenomena on linear and circular DNA molecules. A splicing system is defined by giving an initial set I and a set R of rules. Some unanswered questions are related to the computational power of circular splicing systems. In particular, a still open question is to find a characterization of circular languages generated by finite circular splicing systems (i.e., circular splicing systems with both I and R finite sets). In this paper we introduce a special class of the latter systems named marked systems. We prove that a marked system S generates a regular circular language if an…
On the regularity of circular splicing languages : A survey and new developments
Circular splicing has been introduced to model a specific recombinant behaviour of circular DNA, continuing the investigation initiated with linear splicing. In this paper we focus on the relationship between regular circular languages and languages generated by finite circular splicing systems. We survey the known results towards a characterization of the intersection between these two classes and provide new contributions on the open problem of finding this characterization. First, we exhibit a non-regular circular language generated by a circular simple system thus disproving a known result in this area. Then we give new results related to a restrictive class of circular splicing systems…
On the decomposition of prefix codes
Abstract In this paper we focus on the decomposition of rational and maximal prefix codes. We present an effective procedure that allows us to decide whether such a code is decomposable. In this case, the procedure also produces the factors of some of its decompositions. We also give partial results on the problem of deciding whether a rational maximal prefix code decomposes over a finite prefix code.
Splicing Systems from Past to Future: Old and New Challenges
A splicing system is a formal model of a recombinant behaviour of sets of double stranded DNA molecules when acted on by restriction enzymes and ligase. In this survey we will concentrate on a specific behaviour of a type of splicing systems, introduced by P\u{a}un and subsequently developed by many researchers in both linear and circular case of splicing definition. In particular, we will present recent results on this topic and how they stimulate new challenging investigations.