Mikhail Barash

Defining contexts in context-free grammars

Conjunctive grammars (Okhotin, 2001) are an extension of the standard context-free grammars with a conjunction operation, which maintains most of their practical properties, including many parsing algorithms. This paper introduces a further extension to the model, which is equipped with quantifiers for referring to the left context, in which the substring being defined does occur. For example, a rule A → a & ◺B defines a string a, as long as it is preceded by any string defined by B. The paper gives two equivalent definitions of the model--by logical deduction and by language equations--and establishes its basic properties, including a transformation to a normal form, a cubic-time parsing algorithm, and another recognition algorithm working in linear space.

Linear grammars with one-sided contexts and their automaton representation

The paper considers a family of formal grammars that extends linear context-free grammars with an operator for referring to the left context of a substring being defined, as well as with a conjunction operation (as in linear conjunctive grammars). These grammars are proved to be computationally equivalent to an extension of one-way real-time cellular automata with an extra data channel. The main result is the undecidability of the emptiness problem for grammars restricted to a one-symbol alphabet, which is proved by simulating a Turing machine by a cellular automaton with feedback. The same construction proves the Σ 0 2 -completeness of the finiteness problem for these grammars and automata.

Generalized LR Parsing Algorithm for Grammars with One-Sided Contexts

The Generalized LR parsing algorithm for context-free grammars is notable for having a decent worst-case running time (cubic in the length of the input string, if implemented efficiently), as well as much better performance on “good” grammars. This paper extends the Generalized LR algorithm to the case of “grammars with left contexts” (M. Barash, A. Okhotin, “An extension of context-free grammars with one-sided context specifications”, Inform. Comput., 2014), which augment the context-free grammars with special operators for referring to the left context of the current substring, along with a conjunction operator (as in conjunctive grammars) for combining syntactical conditions. All usual components of the LR algorithm, such as the parsing table, shift and reduce actions, etc., are extended to handle the context operators. The resulting algorithm is applicable to any grammar with left contexts and has the same worst-case cubic-time performance as in the case of context-free grammars.

Generalized LR Parsing for Grammars with Contexts

The Generalized LR parsing algorithm for context-free grammars is notable for having a decent worst-case running time (cubic in the length of the input string), as well as much better performance on “good” grammars. This paper extends the Generalized LR algorithm to the case of “grammars with left contexts” (M. Barash, A. Okhotin, “An extension of context-free grammars with one-sided context specifications”, Inform. Comput., 2014), which augment the context-free grammars with special operators for referring to the left context of the current substring, as well as with a conjunction operator (as in conjunctive grammars) for combining syntactical conditions. All usual components of the LR algorithm, such as the parsing table, shift and reduce actions, etc., are extended to handle the context operators. The resulting algorithm is applicable to any grammar with left contexts and has the same worst-case cubic-time performance as in the case of context-free grammars.

Linear Grammars with One-Sided Contexts and Their Automaton Representation

The paper considers a family of formal grammars that extends linear context-free grammars with an operator for referring to the left context of a substring being defined, as well as with a conjunction operation (as in linear conjunctive grammars). These grammars are proved to be computationally equivalent to an extension of one-way real-time cellular automata with an extra data channel. The main result is the undecidability of the emptiness problem for grammars restricted to a one-symbol alphabet, which is proved by simulating a Turing machine by a cellular automaton with feedback. The same construction proves the \(\Sigma^0_2\)-completeness of the finiteness problem for these grammars.

Linear-space recognition for grammars with contexts

Grammars with contexts are an extension of context-free grammars equipped with operators for referring to the left and the right contexts of a substring being defined. These grammars are notable for still having a cubic-time parsing algorithm, as well as for being able to describe some useful syntactic constructs, such as declaration before use. It is proved in this paper that every language described by a grammar with contexts can be recognized in deterministic linear space.

A Foundational Framework for Step-by-step Model Construction

Constructing large biomodels de-novo is a computationally expensive process, requiring large sets of high-quality data. An alternative approach is to construct them from smaller existing models through various operations such as union, intersection, difference, and refinement. We introduce in this paper a foundational framework for biomodel construction capturing these operations, and we discuss some of their properties.