Parallel communicating finite automata (PCFAs) are systems of several finite state automata which process a common input string in a parallel way and are able to communicate by sending their states upon request. We consider deterministic and nondeterministic variants and distinguish four working modes. It is known that these systems in the most general mode are as powerful as one-way multi-head finite automata. It is additionally known that the number of heads corresponds to the number of automata in PCFAs in a constructive way. Thus, undecidability results as well as results on the hierarchies induced by the number of heads carry over from multi-head finite automata to PCFAs in the most general mode. Here, we complement these undecidability and hierarchy results also for the remaining working modes. In particular, we show that classical decidability questions are not semi-decidable for any type of PCFAs under consideration. Moreover, it is proven that the number of automata in the system induces infinite hierarchies for deterministic and nondeterministic PCFAs in three working modes.
Systems of parallel finite automata communicating by states are investigated. We consider deterministic and nondeterministic devices and distinguish four working modes. It is known that systems in the most general mode are as powerful as one-way multi-head finite automata. Here we solve some open problems on the computational capacity of systems working in the remaining modes. In particular, it is shown that deterministic returning and non-returning devices are equivalent, and that there are languages which are accepted by deterministic returning and centralized systems but cannot be accepted by deterministic non-returning centralized systems. Furthermore, we show that nondeterministic systems are strictly more powerful than their deterministic variants in all the four working modes. Finally, incomparability with the classes of (deterministic) (linear) context-free languages as well as the Church-Rosser languages is derived. . 713 Int. J. Found. Comput. Sci. 2012.23:713-732. Downloaded from www.worldscientific.com by CHINESE UNIVERSITY OF HONG KONG on 02/06/15. For personal use only. 714 H. Bordihn, M. Kutrib & A. Malchersequential processes. To obtain such a theory also for cooperating systems, it is an obvious generalization to proceed from one sequential automaton to systems of sequential automata. Some questions immediately arising are, for example, whether the input is processed in a parallel or sequential way and how the input is accepted. One may ask how the cooperation between different automata is organized and whether they work in a synchronous or an asynchronous way. One has to define in which way communication between different automata takes place and how appropriate restrictions on the amount of information communicated can be formulated.In the literature, systems of cooperating sequential automata appear in many facets. Multi-head finite automata [13] are in some sense the simplest model of cooperating automata, since a finite automaton is provided with a fixed number of reading heads. So, we have some model with one finite state control and the cooperation between the finite state control and the single components is the reading of the input and positioning the heads. This model is generalized to multi-head two-way finite automata [7] and multi-head pushdown automata [6]. Multi-processor automata [2] are in a way restricted multi-head finite automata, and the relation between both classes is investigated in [5]. Systems of different finite automata communicating by appropriate protocols are described in [1, 10], and systems of cooperating finite automata working in parallel are introduced in [11]. Apart from systems of cooperating automata there is also the broad field of systems of cooperating grammars [4].Here, we will focus on parallel communicating finite automata systems which were introduced in [11]. In this model, the input is read and processed in parallel by several finite automata. The communication between automata is defined in such a way that an automaton can request the current state...
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