Distinguishing extended finite state machine configurations using predicate abstraction

Abstract

Background: Extended Finite State Machines (EFSMs) provide a powerful model for the derivation of functional tests for software systems and protocols. Many EFSM based testing problems, such as mutation testing, fault diagnosis, and test derivation involve the derivation of input sequences that distinguish configurations of a given EFSM specification. Method and Results: In this paper, a method is proposed for the derivation of a distinguishing sequence for two explicitly given or symbolically represented, possibly infinite, sets of EFSM configurations using a corresponding FSM abstraction that is derived based on finite sets of predicates and parameterized inputs. An abstraction function that maps configurations and transitions of the EFSM specification to corresponding abstract states and transitions of the abstraction FSM is proposed. Properties of the abstraction are established along with a discussion on a proper selection of the sets of predicates and parameterized inputs used while deriving an FSM abstraction. If no distinguishing sequence is found for the current FSM abstraction then a refined abstraction is constructed by extending the sets of predicates and parameterized inputs. Simple heuristics for the selection of additional predicates are discussed and application examples are provided. Conclusions: The work can be applied in various domains such as EFSM-based test derivation, mutation testing, and fault diagnosis.

Deriving Test Suites with the Guaranteed Fault Coverage for Extended Finite State Machines

“…Недетерминированные автоматы появляются и при рассмотрении предикатных абстракций расширенных автома-тов [16]; при построении различающих последовательностей такие абстракции ока-зываются наиболее эффективными при отсутствии входных параметров.…”

“…Упрощая утверждение из работы [16] для случая различимости начальных конфигураций двух расширенных автоматов, получаем, что два расширенных автомата различимы (адаптивной) входной последовательностью α, если начальные состояния соответ-ствующих предикатных абстракций разделимы последовательностью α (адаптивно различимы), т.е. множества выходных реакций на α в этих состояниях не пересека-ются (существует адаптивный различающий тестовый пример [15]).…”

“…множества выходных реакций на α в этих состояниях не пересека-ются (существует адаптивный различающий тестовый пример [15]). В работе [16] об-суждаются возможности выбора предикатов (для построения предикатной абстрак-ции) с целью уменьшения недетерминизма, чтобы увеличить вероятность существо-вания разделяющей последовательности. Кроме того, можно строить адаптивную различающую последовательность, т.е.…”

Increasing the Fault Coverage of Tests Derived Against Extended Finite State Machines

“…As shown in [19], in this case, a distinguishing sequence will be constructed for two nondeterministic FSMs. It is also the case when predicate abstractions are considered when deriving a distinguishing sequence [20]. One of simple ways is to use l-equivalents of an EFSM which describe the EFSM behavior under critical (parameterized) input sequences of length up to l. In the paper [10], it is experimentally shown that when two EFSMs differ in a small number of transitions (the specification EFSM and a mutant EFSM with one or two mutation transitions) usually it is enough to consider l = 2, 3 when deriving a distinguishing sequence.…”

Multiple Mutation Testing from Finite State Machines with Symbolic Inputs

“…In the automotive applications, the behaviors of some controllers [18] depend on the truth values of predicates defined over input variables with infinite domains. Extensions of FSMs with symbolic inputs and arithmetic operations on variables have been proposed [3,21,14] to relax limitations of the classical FSM and used in developing testing methods [9,21,14]. Following the same trend, our test generation method by constraint solving from FSM in [19,20] could be enhanced to extended FSM.…”