D. G. Thomas

Algebraic properties of the shuffle over ω-trajectories

Algebraic properties of a relation on ω-words based on the notion of shuffle over ω-trajectories are obtained.

Learning code regular and code linear languages

In this paper, a subclass of regular languages, called code regular languages is defined. Algorithms for learning these languages are presented in the frame work of identification in the limit. Learning of analogous subclass of linear languages is also examined.

Public Key Cryptosystems Based on Free Partially Commutative Monoids and Groups

A public key cryptosystem based on free partially commutative monoids is constructed. The encryption of a message to create the cryptotext uses a Thue system which is formed from the free partially commutative monoid with the help of a trapdoor morphism. The decidability of the word problem for free partially commutative monoids can be used for decryption. Finding the trapdoor morphism of this system is shown to be NP-hard. But, a zero – knowledge protocol to convince a verifier that there is such a trapdoor morphism is provided. A related but different public key cryptosystem based on free partially commutative groups is also proposed.

Inferring Subclasses of Contextual Languages

In this paper, we show that the languages generated by internal contextual grammars are not inferable from positive data only. We define two subclasses of internal contextual languages, namely, k-uniform and strictly internal contextual languages which are incomparable classes and provide an algorithm to learn these classes. The algorithm can be used when the rules are applied in a parallel mode.

Learning a Subclass of Context-Free Languages

In this paper, Apical growth Pure context-free grammars (AGPCFG) which are a variation of the pure grammars of Maurer et al are introduced. These grammars allow rewriting of active symbols at the ends of a string simultaneously. They also provide a variation of another kind of grammars called filamentous systems with apical growth, which are motivated by biological considerations. The family of languages generated by AGPCFGs is a subclass of context-free languages. An algorithm for learning this language subclass, in the framework of identification in the limit from positive examples, is provided.

Learning of Regular Bi-ω Languages

In this paper, we define three classes of languages of bi-infinite words, namely local bi-ω languages, recognizable bi-ω languages and Buchi local bi-ω languages as subclasses of the class of regular bi-ω languages and prove some basic results. We observe that the class of recognizable bi-ω languages coincides with the well-known class of rational bi-adherence languages and show that the class of regular bi-ω languages is the class of morphic images of Buchi local bi-ω languages. We provide learning algorithms for Buchi local bi-ω languages and regular bi-ω languages.

A note on inferring uniquely terminating code languages

A subclass of linear languages, called uniquely terminating code linear languages (utCLL), is introduced, motivated by the study of Makinen (1997), and an inference algorithm for utCLL is provided. The algorithm is extended to a corresponding subclass of equal matrix languages.

Learning of church-Rosser tree rewriting systems

Tree rewriting systems are sets of tree rewriting rules used to compute by repeatedly replacing equal trees in a given formula until the simplest possible form (normal form) is obtained. The Church-Rosser property is certainly one of the most fundamental properties of tree rewriting system. In this system the simplest form of a given tree is unique since the final result does not depend on the order in which the rewritings rules are applied. The Church-Rosser system can offer both flexible computing and effecting reasoning with equations and have been intensively researched and widely applied to automated theorem proving and program verification etc. [3,5].

Learning subclasses of parallel communicating grammar systems

Pattern language learning algorithms within the inductive inference model and query learning setting have been of great interest. In this paper an algorithm to learn a parallel communicating grammar system in which the master component is a regular grammar and the other components are pure pattern grammars is given.