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

Propagating Regular Counting Constraints

Constraints over finite sequences of variables are ubiquitous in sequencing and timetabling. Moreover, the wide variety of such constraints in practical applications led to general modelling techniques and generic propagation algorithms, often based on deterministic finite automata (DFA) and their extensions. We consider counter-DFAs (cDFA), which provide concise models for regular counting constraints, that is constraints over the number of times a regular-language pattern occurs in a sequence. We show how to enforce domain consistency in polynomial time for atmost and atleast regular counting constraints based on the frequent case of a cDFA with only accepting states and a single counter that can be incremented by transitions. We also prove that the satisfaction of exact regular counting constraints is NP-hard and indicate that an incomplete algorithm for exact regular counting constraints is faster and provides more pruning than the existing propagator from [3]. Regular counting constraints are closely related to the CostRegular constraint but contribute both a natural abstraction and some computational advantages.Comment: Includes a SICStus Prolog source file with the propagato

Process mining meets model learning: Discovering deterministic finite state automata from event logs for business process analysis

Within the process mining field, Deterministic Finite State Automata (DFAs) are largely employed as foundation mechanisms to perform formal reasoning tasks over the information contained in the event logs, such as conformance checking, compliance monitoring and cross-organization process analysis, just to name a few. To support the above use cases, in this paper, we investigate how to leverage Model Learning (ML) algorithms for the automated discovery of DFAs from event logs. DFAs can be used as a fundamental building block to support not only the development of process analysis techniques, but also the implementation of instruments to support other phases of the Business Process Management (BPM) lifecycle such as business process design and enactment. The quality of the discovered DFAs is assessed wrt customized definitions of fitness, precision, generalization, and a standard notion of DFA simplicity. Finally, we use these metrics to benchmark ML algorithms against real-life and synthetically generated datasets, with the aim of studying their performance and investigate their suitability to be used for the development of BPM tools

Learning DFA for Simple Examples

We present a framework for learning DFA from simple examples. We show that efficient PAC learning of DFA is possible if the class of distributions is restricted to simple distributions where a teacher might choose examples based on the knowledge of the target concept. This answers an open research question posed in Pitt\u27s seminal paper: Are DFA\u27s PAC-identifiable if examples are drawn from the uniform distribution, or some other known simple distribution? Our approach uses the RPNI algorithm for learning DFA from labeled examples. In particular, we describe an efficient learning algorithm for exact learning of the target DFA with high probability when a bound on the number of states (N) of the target DFA is known in advance. When N is not known, we show how this algorithm can be used for efficient PAC learning of DFAs