Learning Moore Machines from Input-Output Traces

The problem of learning automata from example traces (but no equivalence or membership queries) is fundamental in automata learning theory and practice. In this paper we study this problem for finite state machines with inputs and outputs, and in particular for Moore machines. We develop three algorithms for solving this problem: (1) the PTAP algorithm, which transforms a set of input-output traces into an incomplete Moore machine and then completes the machine with self-loops; (2) the PRPNI algorithm, which uses the well-known RPNI algorithm for automata learning to learn a product of automata encoding a Moore machine; and (3) the MooreMI algorithm, which directly learns a Moore machine using PTAP extended with state merging. We prove that MooreMI has the fundamental identification in the limit property. We also compare the algorithms experimentally in terms of the size of the learned machine and several notions of accuracy, introduced in this paper. Finally, we compare with OSTIA, an algorithm that learns a more general class of transducers, and find that OSTIA generally does not learn a Moore machine, even when fed with a characteristic sample

Automated unique input output sequence generation for conformance testing of FSMs

This paper describes a method for automatically generating unique input output (UIO) sequences for FSM conformance testing. UIOs are used in conformance testing to verify the end state of a transition sequence. UIO sequence generation is represented as a search problem and genetic algorithms are used to search this space. Empirical evidence indicates that the proposed method yields considerably better (up to 62% better) results compared with random UIO sequence generation

Automata Minimization: a Functorial Approach

In this paper we regard languages and their acceptors - such as deterministic or weighted automata, transducers, or monoids - as functors from input categories that specify the type of the languages and of the machines to categories that specify the type of outputs. Our results are as follows: A) We provide sufficient conditions on the output category so that minimization of the corresponding automata is guaranteed. B) We show how to lift adjunctions between the categories for output values to adjunctions between categories of automata. C) We show how this framework can be instantiated to unify several phenomena in automata theory, starting with determinization, minimization and syntactic algebras. We provide explanations of Choffrut's minimization algorithm for subsequential transducers and of Brzozowski's minimization algorithm in this setting.Comment: journal version of the CALCO 2017 paper arXiv:1711.0306

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Decidability and Universality in Symbolic Dynamical Systems

Many different definitions of computational universality for various types of dynamical systems have flourished since Turing's work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical systems. Universality of a system is defined as undecidability of a model-checking problem. For Turing machines, counter machines and tag systems, our definition coincides with the classical one. It yields, however, a new definition for cellular automata and subshifts. Our definition is robust with respect to initial condition, which is a desirable feature for physical realizability. We derive necessary conditions for undecidability and universality. For instance, a universal system must have a sensitive point and a proper subsystem. We conjecture that universal systems have infinite number of subsystems. We also discuss the thesis according to which computation should occur at the `edge of chaos' and we exhibit a universal chaotic system.Comment: 23 pages; a shorter version is submitted to conference MCU 2004 v2: minor orthographic changes v3: section 5.2 (collatz functions) mathematically improved v4: orthographic corrections, one reference added v5:27 pages. Important modifications. The formalism is strengthened: temporal logic replaced by finite automata. New results. Submitte

Towards a Church-Turing-Thesis for Infinitary Computations

We consider the question whether there is an infinitary analogue of the Church-Turing-thesis. To this end, we argue that there is an intuitive notion of transfinite computability and build a canonical model, called Idealized Agent Machines ($IAM$s) of this which will turn out to be equivalent in strength to the Ordinal Turing Machines defined by P. Koepke

Improved test quality using robust unique input/output circuit sequences (UIOCs)

In finite state machine (FSM) based testing, the problem of fault masking in the unique input/ output (UIO) sequence may degrade the test performance of the UIO based methods. This paper investigates this problem and proposes the use of a new type of unique input/output circuit (UIOC) sequence for state verification, which may help to overcome the drawbacks that exist in the UIO based techniques. When constructing a UIOC, overlap and internal state observation schema are used to increase the robustness of a test sequence. Test quality is compared by using the forward UIO method (F-method), the backward UIO method (B-method) and the UIOC method (C-method) separately. Robustness of the UIOCs constructed by the algorithm given in this paper is also compared with those constructed by the algorithm given previously. Experimental results suggest that the C-method outperforms the F- and the B-methods and the UIOCs constructed by the Algorithm given in this paper, are more robust than those constructed by other proposed algorithms

Constructing multiple unique input/output sequences using metaheuristic optimisation techniques

Multiple unique input/output sequences (UIOs) are often used to generate robust and compact test sequences in finite state machine (FSM) based testing. However, computing UIOs is NP-hard. Metaheuristic optimisation techniques (MOTs) such as genetic algorithms (GAs) and simulated annealing (SA) are effective in providing good solutions for some NP-hard problems. In the paper, the authors investigate the construction of UIOs by using MOTs. They define a fitness function to guide the search for potential UIOs and use sharing techniques to encourage MOTs to locate UIOs that are calculated as local optima in a search domain. They also compare the performance of GA and SA for UIO construction. Experimental results suggest that, after using a sharing technique, both GA and SA can find a majority of UIOs from the models under test