Distributed-Automata and Simple Test Tube Systems

In classical Formal Language Theory, “centralised” grammar systems and automata were the standard models for computation devices. With the rapid growth of computer networks, distributed databases, etc, distributed computation has begun to play a major role in modern computer science. The theory of grammar systems and distributed-automata was thus developed as a model for distributed computation. In this thesis, we introduce the notion of distributed-automata. DistributedAutomata are a group of automata working in unison to accept one language. We build the theory of distributed-automata for specific automata like FSA, PDA and k-turn PDA. We then analyse the acceptance capacity of each of these automata. We present proofs that distributed FSA do not have any additional power over “centralised” FSA while both distributed PDAs and k-turn PDAs with just two components working together are as powerful as Turing Machines. We then extend the definition of test tube systems to simple H systems and analyse their generative capacity. Distributed simple H systems are a group of simple H systems working in parallel with an architecture similar to that of PC grammar systems. Though simple H systems generate only regular languages, we show that when these systems work in parallel, with the aid of morphisms and intersection with regular sets, they are able to characterise all context-free languages.