Formal language

About: Formal language is a research topic. Over the lifetime, 5763 publications have been published within this topic receiving 154114 citations.

Criticality in Formal Languages and Statistical Physics

Abstract: We show that the mutual information between two symbols, as a function of the number of symbols between the two, decays exponentially in any probabilistic regular grammar, but can decay like a power law for a context-free grammar. This result about formal languages is closely related to a well-known result in classical statistical mechanics that there are no phase transitions in dimensions fewer than two. It is also related to the emergence of power-law correlations in turbulence and cosmological inflation through recursive generative processes. We elucidate these physics connections and comment on potential applications of our results to machine learning tasks like training artificial recurrent neural networks. Along the way, we introduce a useful quantity which we dub the rational mutual information and discuss generalizations of our claims involving more complicated Bayesian networks.

Formal Semantics of Synchronous SystemC

Abstract: In this article, a denotational definition of a synchronous subset of SystemC is proposed. The subset treated includes modules, processes, threads, wait statement, ports and signals. We propose a formal model for SystemC delta delay. Also, we give a complete semantic definition for the language's two-phase scheduler. The proposed semantic can constitute a base for validating the equivalence of synchronous HDL subsets.

On the Temporal Granularity in Fuzzy Cognitive Maps

Abstract: The theory of fuzzy cognitive maps (FCMs) is a powerful approach to modeling human knowledge that is based on causal reasoning. Taking advantage of fuzzy logic and cognitive map theories, FCMs enable system designers to model complex frameworks by defining degrees of causality between causal objects. They can be used to model and represent the behavior of simple and complex systems by capturing and emulating the human being to describe and present systems in terms of tolerance, imprecision, and granulation of information. However, FCMs lack the temporal concept that is crucial in many real-world applications, and they do not offer formal mechanisms to verify the behavior of systems being represented, which limit conventional FCMs in knowledge representation. In this paper, we present an extension to FCMs by exploiting a theory from formal languages, namely, the timed automata, which bridges the aforementioned inadequacies. Indeed, the theory of timed automata enables FCMs to effectively deal with a double-layered temporal granularity, extending the standard idea of B-time that characterizes the iterative nature of a cognitive inference engine and offering model checking techniques to test the cognitive and dynamic comportment of the framework being designed.

The application of formal methods to the assessment of high integrity software

Abstract: A case study is presented in which the Vienna development method (VDM), a formal specification and development methodology, was used during the analysis phase of the assessment of a prototype nuclear reactor protection system. The VDM specification was also translated into the logic language Prolog to animate the specification and to provide a diverse implementation for use in back-to-back testing. It is claimed that this technique provides a visible and effective method of analysis which is superior to the informal alternatives.

Expressiveness and Closure Properties for Quantitative Languages

Abstract: Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages L that assign to each word w a real number L(w). In the case of infinite words, the value of a run is naturally computed as the maximum, limsup, liminf, limit average, or discounted sum of the transition weights. We study expressiveness and closure questions about these quantitative languages. We first show that the set of words with value greater than a threshold can be non-omega-regular for deterministic limit-average and discounted-sum automata, while this set is always omega-regular when the threshold is isolated (i.e., some neighborhood around the threshold contains no word). In the latter case, we prove that the omega-regular language is robust against small perturbations of the transition weights. We next consider automata with transition weights 0 or 1 and show that they are as expressive as general weighted automata in the limit-average case, but not in the discounted-sum case. Third, for quantitative languages L1 and L2, we consider the operations max(L1, L2), min(L1, L2), and 1-L1, which generalize the boolean operations on languages, as well as the sum L1 + L2. We establish the closure properties of all classes of quantitative languages with respect to these four operations.