Formal language

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

Learning k-Testable and k-Piecewise Testable Languages from Positive Data.

Abstract: The families of locally testable (LT ) and piecewise testable (PWT ) languages have been deeply studied in formal language theory. They have in common that the role played by the segments of length k of their words in the first family is played in the second by their subwords (sequences of non necessarily consecutive symbols), also of length k. We propose algorithms that, given k > 0, identify both families of languages (k-PWT and k-LT ) from positive data in the limit. The first one identifies the family of k-PWT languages making use of a combinatorial property discovered by Simon and improves the complexity of a previous algorithm for that family [25]. The second algorithm identifies the family of k-LT languages using a result about the cascade product of automata. In this product, for each k, one of the factors is a fixed transducer and the second is the automaton obtained by the first algorithm for k = 1 using the transduction of the sample as input.

LISA: a tool for automatic language implementation

Abstract: In the paper a tool for automatic language implementation is described. From formal language definition LISA1 produces efficient interpreters or compilers in C++. For lexical and syntax analysis well known formal methods: regular expressions and BNF are used. Semantics of the defined language is described with attribute grammars. LISA is a part of the ongoing effort to build an environment that supports experimentation in automatic language implementation for educational and industrial purposes.

Systems and methods for regularly approximating context-free grammars through transformation

Abstract: Context-free grammars generally comprise a large number of rules, where each rule defines how a string of symbols is generated from a different series of symbols. While techniques for creating finite-state automata from the rules of context-free grammars exist, these techniques require an input grammar to be strongly regular. Systems and methods that convert the rules of a context-free grammar into a strongly regular grammar include transforming each input rule into a set of output rules that approximate the input rule. The output rules are all right- or left-linear and are strongly regular. In various exemplary embodiments, the output rules are output in a specific format that specifies, for each rule, the left-hand non-terminal symbol, a single right-hand non-terminal symbol, and zero, one or more terminal symbols. If the input context-free grammar rule is weighted, the weight of that rule is distributed and assigned to the output rules.

Languages that are easier than their proofs

Abstract: Languages in NP are presented for which it is harder to prove membership interactively than it is to decide this membership. Similarly, languages where checking is harder than computing membership are presented. Under assumptions about triple-exponential time, incoherent sets in NP are constructed. Without any assumptions, incoherent sets are constructed in DSPACE (n to the log n), yielding the first uncheckable and non-random-self-reducible sets in that space. >