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## Automata system: determinism conditions and testing

#### Abstract

The problem of testing of aggregate systems is considered. The system components are described with finite automata with multiple entries and exits. The communication between automata is described with message passing over simplex communication channels. The system is described with an oriented graph of links. Each node of the graph corresponds to automaton of a component and an arc corresponds to a communication channel connecting exit of one automaton with entry of another automaton. The hypothesis of the links is assumed: the graph of links is static and the link structure is error-free. Automaton of the graph node in each state can accept multiple messages from its entries (at most one message from each entry) and send multiple messages to its exits (at most one message to each exit). An associative composition of the automata is defined. The restrictions on the automata and the graph of links are determined, for which their composition, i.e. the system itself, is deterministic. The goal of testing is to cover transitions of the automata reachable during the system work. It assumed that during testing it is possible to observe the states of automata and the messages on the arcs. The complete testing of the automata system without considering the hypothesis of links may require the number of testing actions of order of multiplication of numbers of states of the component automata, while with the consideration of the hypothesis of links – of order of the sum of these numbers. If the numbers of states of all automata are equal, it gives exponential reduction of the number of test actions. If the hypothesis of links is true, an algorithm of test generation for a deterministic system is proposed basing on filtration of tests generated for covering all transitions of the composition. Test is rejected if it covers only such transitions of the components that are covered by the remaining tests. In conclusion, the directions of future research are described.

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#### Edition

Proceedings of the Institute for System Programming, vol. 28, issue 1, 2016, pp. 151-184.

ISSN 2220-6426 (Online), ISSN 2079-8156 (Print).

DOI: 10.15514/ISPRAS-2016-28(1)-9

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