Daniela Genova

Defining languages by forbidding-enforcing systems

Motivated by biomolecular computing, forbidding-enforcing systems (fe-systems) were first used to define classes of languages (fefamilies) based on boundary conditions. This paper presents a new model of fe-systems in which fe-systems define single languages (fe-languages) based on forbidden and enforced subwords. The paper characterizes well-known languages by fe-systems, investigates the relationship between fefamilies and fe-languages, and describes how an fe-system can generate the solution to the k-colorability problem and model splicing.

Forbidding sets and normal forms for language forbidding-enforcing systems

This paper investigates ways to reduce redundancy in forbidding sets for language forbidding-enforcing systems. A language forbidding set disallows combinations of subwords in a word, while permitting the presence of some parts of these combinations. Since a forbidding set is a potentially infinite set of finite sets of words, finding normal forms for forbidding sets is interesting from a combinatorics on words perspective and important for the theoretical investigation of language fe-systems, the connection between variants of fe-systems, and their applications to molecular computation. This paper shows that the minimal normal forms for forbidding sets defining classes of languages (fe-families) are also normal forms for forbidding sets defining single languages (fe-languages), but not necessarily minimal. Thus, an investigation of minimality and sufficient conditions for fe-languages are presented and it is shown that in special cases they coincide with a minimal normal form for fe-families.

Forbidding and enforcing on graphs

We define classes of graphs based on forbidding and enforcing boundary conditions. Forbidding conditions prevent a graph to have certain combinations of subgraphs and enforcing conditions impose certain subgraph structures. We say that a class of graphs is an fe-class if the class can be defined through forbidding and enforcing conditions (fe-system). We investigate properties of fe-systems and characterize familiar classes of graphs such as paths and cycles, trees, bi-partite, complete, Eulerian, and k-regular graphs as fe-classes.

Generating DNA code words using forbidding and enforcing systems

Research in DNA computing was initiated by Leonard Adleman in 1994 when he solved an instance of an NP-complete problem solely by molecules. DNA code words arose in the attempt to avoid unwanted hybridizations of DNA strands for DNA based computations. Given a set of constraints, generating a large set of DNA strands that satisfy the constraints is an important problem in DNA computing. On the other hand, motivated by the non-determinism of molecular reactions, A. Ehrenfeucht and G. Rozenberg introduced forbidding and enforcing systems (fe-systems) as a model of computation that defines classes of languages based on two sets of constraints. We attempt to establish a connection between these two areas of research in natural computing by characterizing a variety of DNA codes that avoid certain types of cross hybridizations by fe-systems. We show that one fe-system can generate the entire class of DNA codes of a certain property, for example θ-k-codes, and confirm some properties of DNA codes through fe-systems. We generalize by fe-systems some known methods of generating good DNA code words which have been tested experimentally.

A graph isomorphism condition and equivalence of reaction systems

We consider global dynamics of reaction systems as introduced by Ehrenfeucht and Rozenberg. The dynamics is represented by a directed graph, the so-called transition graph, and two reaction systems are considered equivalent if their corresponding transition graphs are isomorphic. We introduce the notion of a skeleton (a one-out graph) that uniquely determines a directed graph. We provide the necessary and sufficient conditions for two skeletons to define isomorphic graphs. This provides a necessary and sufficient condition for two reactions systems to be equivalent, as well as a characterization of the directed graphs that correspond to the global dynamics of reaction systems.

Language Forbidding-Enforcing Systems Defining DNA Codewords

DNA code word design is an interesting and important area of research in DNA computing and generating a large set of DNA strands that satisfy a given set of constraints is a difficult and important problem. On the other hand, forbidding and enforcing systems (fe-systems) are a molecularly inspired model of computation that defines structures based on constraints. This paper reinforces the connection between fe-systems and DNA codes by using the single language model of fe-systems to characterize a variety of DNA codes that avoid certain types of cross hybridizations. Some known methods of generating good DNA code words which have been tested experimentally are generalized by fe-systems. Finally, it is shown how the theoretical definitions by fe-systems can be used as a computational tool and also to model laboratory experiments.

Finite Language Forbidding-Enforcing Systems

The forbidding and enforcing paradigm was introduced by Ehrenfeucht and Rozenberg as a way to define families of languages based on two sets of boundary conditions. Later, a variant of this paradigm was considered where an fe-system defines a single language. We investigate this variant further by studying fe-systems in which both the forbidding and enforcing sets are finite and show that they define regular languages. We prove that the class of languages defined by finite fe-systems is strictly between the strictly locally testable languages and the class of locally testable languages.