Inference Of Regular Languages Research Articles

Meta-interpretive learning: application to grammatical inference

Despite early interest Predicate Invention has lately been under-explored within ILP. We develop a framework in which predicate invention and recursive generalisations are implemented using abduction with respect to a meta-interpreter. The approach is based on a previously unexplored case of Inverse Entailment for Grammatical Inference of Regular languages. Every abduced grammar H is represented by a conjunction of existentially quantified atomic formulae. Thus ¬H is a universally quantified clause representing a denial. The hypothesis space of solutions for ¬H can be ordered by ?-subsumption. We show that the representation can be mapped to a fragment of Higher-Order Datalog in which atomic formulae in H are projections of first-order definite clause grammar rules and the existentially quantified variables are projections of first-order predicate symbols. This allows predicate invention to be effected by the introduction of first-order variables. Previous work by Inoue and Furukawa used abduction and meta-level reasoning to invent predicates representing propositions. By contrast, the present paper uses abduction with a meta-interpretive framework to invent relations. We describe the implementations of Meta-interpretive Learning (MIL) using two different declarative representations: Prolog and Answer Set Programming (ASP). We compare these implementations against a state-of-the-art ILP system MC-TopLog using the dataset of learning Regular and Context-Free grammars as well learning a simplified natural language grammar and a grammatical description of a staircase. Experiments indicate that on randomly chosen grammars, the two implementations have significantly higher accuracies than MC-TopLog. In terms of running time, Metagol is overall fastest in these tasks. Experiments indicate that the Prolog implementation is competitive with the ASP one due to its ability to encode a strong procedural bias. We demonstrate that MIL can be applied to learning natural grammars. In this case experiments indicate that increasing the available background knowledge, reduces the running time. Additionally ASPM (ASP using a meta-interpreter) is shown to have a speed advantage over Metagol when background knowledge is sparse. We also demonstrate that by combining MetagolR (Metagol with a Regular grammar meta-interpreter) and MetagolCF (Context-Free meta-interpreter) we can formulate a system, MetagolRCF, which can change representation by firstly assuming the target to be Regular, and then failing this, switch to assuming it to be Context-Free. MetagolRCF runs up to 100 times faster than MetagolCF on grammars chosen randomly from Regular and non-Regular Context-Free grammars.

Regular Model Checking Using Inference of Regular Languages

Regular model checking is a method for verifying infinite-state systems based on coding their configurations as words over a finite alphabet, sets of configurations as finite automata, and transitions as finite transducers. We introduce a new general approach to regular model checking based on inference of regular languages. The method builds upon the observation that for infinite-state systems whose behaviour can be modelled using length-preserving transducers, there is a finite computation for obtaining all reachable configurations up to a certain length n. These configurations are a (positive) sample of the reachable configurations of the given system, whereas all other words up to length n are a negative sample. Then, methods of inference of regular languages can be used to generalize the sample to the full reachability set (or an overapproximation of it). We have implemented our method in a prototype tool which shows that our approach is competitive on a number of concrete examples. Furthermore, in contrast to all other existing regular model checking methods, termination is guaranteed in general for all systems with regular sets of reachable configurations. The method can be applied in a similar way to dealing with reachability relations instead of reachability sets too.

Inference of regular languages using state merging algorithms with search

State merging algorithms have emerged as the solution of choice for the problem of inferring regular grammars from labeled samples, a known NP-complete problem of great importance in the grammatical inference area. These methods derive a small deterministic finite automaton from a set of labeled strings (the training set), by merging parts of the acceptor that corresponds to this training set. Experimental and theoretical evidence have shown that the generalization ability exhibited by the resulting automata is highly correlated with the number of states in the final solution. As originally proposed, state merging algorithms do not perform search. This means that they are fast, but also means that they are limited by the quality of the heuristics they use to select the states to be merged. Sub-optimal choices lead to automata that have many more states than needed and exhibit poor generalization ability. In this work, we survey the existing approaches that generalize state merging algorithms by using search to explore the tree that represents the space of possible sequences of state mergings. By using heuristic guided search in this space, many possible state merging sequences can be considered, leading to smaller automata and improved generalization ability, at the expense of increased computation time. We present comparisons of existing algorithms that show that, in widely accepted benchmarks, the quality of the derived solutions is improved by applying this type of search. However, we also point out that existing algorithms are not powerful enough to solve the more complex instances of the problem, leaving open the possibility that better and more powerful approaches need to be designed.

ON THE USE OF THE MORPHIC GENERATOR GRAMMATICAL INFERENCE (MGGI) METHODOLOGY IN AUTOMATIC SPEECH RECOGNITION

Recently, a new methodology, referred to as “Morphic Generator Grammatical Inference” (MGGI), has been introduced as a step towards a general methodology for the inference of regular languages. In this paper we consider the application of this methodology to a real problem of automatic speech recognition, thus allowing (and also requiring) the proposed problem to be properly formulated within the canonical framework of syntactic pattern recognition. The results show both the viability and appropriateness of the application of MGGI to the problem considered.

Inductive inference of regular languages based on model inference

This paper is concerned with an algorithm for identifying an unknown regular language from examples of its members and non-members. The algorithm is based on the model inference algorithm given by Shapiro. In our setting, however, a given first order language for describing a target logic program has countably many unary predicate symbols: q 0,q 1,q 2…. On the other hand, the oracle which gives information about the unknown regular language to the inference algorithm has no interpretation for predicates other than the predicate q 0. In such a setting,we cannot directly take advantage of the contradiction backtracing algorithm which is one of the most important parts for the efficiency of the model inference algorithm. In order to overcome this disadvantage, we develop a method for giving an interpretation for predicates other than the predicate q 0 indirectly, which is based on the idea of using the oracle and a one to one mapping from a set of predicates to a set of strings. Furthermore, we propose a mod...