Inference of regular languages using model simplicity

We describe an approach that is related to a number of existing algorithms for the inference of a regular language from a set of positive (and optionally also negative) examples. Variations on this approach provide a family of algorithms that attempt to minimise the complexity of a description of the example data in terms of a finite state automaton model. Experiments using a standard set of small problems show that this approach produces satisfactory results when positive examples only are given, and can be helpful when only a limited number of negative examples is available. The results also suggest that improved algorithms will be needed in order to tackle more challenging problems, such as data mining and exploratory sequential analysis application

Inducing Probabilistic Grammars by Bayesian Model Merging

We describe a framework for inducing probabilistic grammars from corpora of positive samples. First, samples are {\em incorporated} by adding ad-hoc rules to a working grammar; subsequently, elements of the model (such as states or nonterminals) are {\em merged} to achieve generalization and a more compact representation. The choice of what to merge and when to stop is governed by the Bayesian posterior probability of the grammar given the data, which formalizes a trade-off between a close fit to the data and a default preference for simpler models (`Occam's Razor'). The general scheme is illustrated using three types of probabilistic grammars: Hidden Markov models, class-based $n$-grams, and stochastic context-free grammars.Comment: To appear in Grammatical Inference and Applications, Second International Colloquium on Grammatical Inference; Springer Verlag, 1994. 13 page

Algebraic Principles for Rely-Guarantee Style Concurrency Verification Tools

We provide simple equational principles for deriving rely-guarantee-style inference rules and refinement laws based on idempotent semirings. We link the algebraic layer with concrete models of programs based on languages and execution traces. We have implemented the approach in Isabelle/HOL as a lightweight concurrency verification tool that supports reasoning about the control and data flow of concurrent programs with shared variables at different levels of abstraction. This is illustrated on two simple verification examples

Coding-theorem Like Behaviour and Emergence of the Universal Distribution from Resource-bounded Algorithmic Probability

Previously referred to as `miraculous' in the scientific literature because of its powerful properties and its wide application as optimal solution to the problem of induction/inference, (approximations to) Algorithmic Probability (AP) and the associated Universal Distribution are (or should be) of the greatest importance in science. Here we investigate the emergence, the rates of emergence and convergence, and the Coding-theorem like behaviour of AP in Turing-subuniversal models of computation. We investigate empirical distributions of computing models in the Chomsky hierarchy. We introduce measures of algorithmic probability and algorithmic complexity based upon resource-bounded computation, in contrast to previously thoroughly investigated distributions produced from the output distribution of Turing machines. This approach allows for numerical approximations to algorithmic (Kolmogorov-Chaitin) complexity-based estimations at each of the levels of a computational hierarchy. We demonstrate that all these estimations are correlated in rank and that they converge both in rank and values as a function of computational power, despite fundamental differences between computational models. In the context of natural processes that operate below the Turing universal level because of finite resources and physical degradation, the investigation of natural biases stemming from algorithmic rules may shed light on the distribution of outcomes. We show that up to 60\% of the simplicity/complexity bias in distributions produced even by the weakest of the computational models can be accounted for by Algorithmic Probability in its approximation to the Universal Distribution.Comment: 27 pages main text, 39 pages including supplement. Online complexity calculator: http://complexitycalculator.com

Towards Parameterized Regular Type Inference Using Set Constraints

We propose a method for inferring \emph{parameterized regular types} for logic programs as solutions for systems of constraints over sets of finite ground Herbrand terms (set constraint systems). Such parameterized regular types generalize \emph{parametric} regular types by extending the scope of the parameters in the type definitions so that such parameters can relate the types of different predicates. We propose a number of enhancements to the procedure for solving the constraint systems that improve the precision of the type descriptions inferred. The resulting algorithm, together with a procedure to establish a set constraint system from a logic program, yields a program analysis that infers tighter safe approximations of the success types of the program than previous comparable work, offering a new and useful efficiency vs. precision trade-off. This is supported by experimental results, which show the feasibility of our analysis