Formal language

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

New Developments in Formal Languages and Applications

Abstract: Basic Notation and Terminology.- Open Problems on Partial Words.- Alignments and Approximate String Matching.- An Introductory Course on Communication Complexity.- Formal Languages and Concurrent Behaviours.- Cellular Automata - A Computational Point of View.- Probabilistic Parsing.- DNA-Based Memories: A Survey.

A Perfect Model for Bounded Verification

Abstract: A class of languages C is perfect if it is closed under Boolean operations and the emptiness problem is decidable. Perfect language classes are the basis for the automata-theoretic approach to model checking: a system is correct if the language generated by the system is disjoint from the language of bad traces. Regular languages are perfect, but because the disjointness problem for CFLs is undecidable, no class containing the CFLs can be perfect. In practice, verification problems for language classes that are not perfect are often under-approximated by checking if the property holds for all behaviors of the system belonging to a fixed subset. A general way to specify a subset of behaviors is by using bounded languages (languages of the form w1* ... wk* for fixed words w1,...,wk). A class of languages C is perfect modulo bounded languages if it is closed under Boolean operations relative to every bounded language, and if the emptiness problem is decidable relative to every bounded language. We consider finding perfect classes of languages modulo bounded languages. We show that the class of languages accepted by multi-head pushdown automata are perfect modulo bounded languages, and characterize the complexities of decision problems. We also show that bounded languages form a maximal class for which perfection is obtained. We show that computations of several known models of systems, such as recursive multi-threaded programs, recursive counter machines, and communicating finite-state machines can be encoded as multi-head pushdown automata, giving uniform and optimal under approximation algorithms modulo bounded languages.

RT-Z: An Integration of Z and timed CSP

Abstract: We present an integration of Z and timed CSP called RT-Z, incorporating the strengths of both formal languages in a coherent frame. To cope with complex systems, RT-Z is equipped with structuring constructs built on top of the integration, because both Z and timed CSP lack appropriate facilities. For RT-Z to be built on formal grounds, a formal semantics is defined based on the denotational semantics of Z and timed CSP.

On Evaluating the Generalization of LSTM Models in Formal Languages

Abstract: Recurrent Neural Networks (RNNs) are theoretically Turing-complete and established themselves as a dominant model for language processing. Yet, there still remains an uncertainty regarding their language learning capabilities. In this paper, we empirically evaluate the inductive learning capabilities of Long Short-Term Memory networks, a popular extension of simple RNNs, to learn simple formal languages, in particular $a^nb^n$, $a^nb^nc^n$, and $a^nb^nc^nd^n$. We investigate the influence of various aspects of learning, such as training data regimes and model capacity, on the generalization to unobserved samples. We find striking differences in model performances under different training settings and highlight the need for careful analysis and assessment when making claims about the learning capabilities of neural network models.

Calculational semantics: Deriving programming theories from equations by functional predicate calculus

Abstract: The objects of programming semantics, namely, programs and languages, are inherently formal, but the derivation of semantic theories is all too often informal, deprived of the benefits of formal calculation “guided by the shape of the formulas.” Therefore, the main goal of this article is to provide for the study of semantics an approach with the same convenience and power of discovery that calculus has given for many years to applied mathematics, physics, and engineering. The approach uses functional predicate calculus and concrete generic functionals; in fact, a small part suffices. Application to a semantic theory proceeds by describing program behavior in the simplest possible way, namely by program equations, and discovering the axioms of the theory as theorems by calculation. This is shown in outline for a few theories, and in detail for axiomatic semantics, fulfilling a second goal of this article. Indeed, a chafing problem with classical axiomatic semantics is that some axioms are unintuitive at first, and that justifications via denotational semantics are too elaborate to be satisfactory. Derivation provides more transparency. Calculation of formulas for ante- and postconditions is shown in general, and for the major language constructs in particular. A basic problem reported in the literature, whereby relations are inadequate for handling nondeterminacy and termination, is solved here through appropriately defined program equations. Several variants and an example in mathematical analysis are also presented. One conclusion is that formal calculation with quantifiers is one of the most important elements for unifying continuous and discrete mathematics in general, and traditional engineering with computing science, in particular.