Distinguishing Sequences for Distributed Testing: Preset Distinguishing Sequences

Robert M Hierons,Uraz Cengiz Türker

doi:10.1093/comjnl/bxw069

Robert M Hierons, Uraz Cengiz Türker

Open Access

https://doi.org/10.1093/comjnl/bxw069

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Abstract

This paper concerns the problem of testing from a finite state machine (FSM) $M$ modelling a system that interacts with its environment at multiple physically distributed interfaces, called ports. We assume that the distributed test architecture is used: there is a local tester at each port, the tester at port $p$ only observes events at $p$ and the testers do not interact during testing. This paper formalizes the notion of an adaptive test strategy and what it means for an adaptive test strategy to be controllable. We provide algorithms to check whether a global strategy is controllable and to generate a controllable adaptive distinguishing sequence (ADS). We prove that controllable ADS existence is PSPACE-Hard and that the problem of deciding whether $M$ has a controllable ADS with length $\ell $ is NP-Hard. In practice, there is likely to be a polynomial upper bound on the length of ADS in which we are interested and for this case the decision problem is NP-Complete.

Highlights

Testing is an important part of the software development process but is typically manual, expensive, and error prone
We present some definitions and observations related to preset distinguishing sequence (PDS) and we give an upper bound on the length of minimal controllable PDSs for C-FSMs5
Many algorithms for automatically generating test sequences from a single-port finite state machine (FSM) M use input sequences that distinguish the states of M and several such automated test generation algorithms use PDSs

Summary

INTRODUCTION

Testing is an important part of the software development process but is typically manual, expensive, and error prone. The initial work on distributed testing found that there can be additional controllability problems in which a local tester cannot determine when to supply an input since it only observes the events at its port [14, 20]. In distributed testing a local tester observes the events at its ports and so a projection of the global trace (sequence of inputs and outputs) that occurred. Hierons proved that when the FSM has multiple ports, it is undecidable whether a set S of states has an ADS or a PDS and this is the case even when we restrict attention to sets containing only two states [33] Despite these negative results, recently Hierons and Turker investigated the problem of deriving controllable ADSs from a multi-port FSM.

PRELIMINARIES

GENERATING A CONTROLLABLE PDS

PDS GENERATION: A SPECIAL CASE

CONCLUSIONS