For decades we have been using Chomsky's generative system of grammars, particularly context-free grammars (CFGs) and regular expressions (REs), to express the syntax of programming languages and protocols. The power of generative grammars to express ambiguity is crucial to their original purpose of modelling natural languages, but this very power makes it unnecessarily difficult both to express and to parse machine-oriented languages using CFGs. Parsing Expression Grammars (PEGs) provide an alternative, recognition-based formal foundation for describing machineoriented syntax, which solves the ambiguity problem by not introducing ambiguity in the first place. Where CFGs express nondeterministic choice between alternatives, PEGs instead use prioritized choice. PEGs address frequently felt expressiveness limitations of CFGs and REs, simplifying syntax definitions and making it unnecessary to separate their lexical and hierarchical components. A linear-time parser can be built for any PEG, avoiding both the complexity and fickleness of LR parsers and the inefficiency of generalized CFG parsing. While PEGs provide a rich set of operators for constructing grammars, they are reducible to two minimal recognition schemas developed around 1970, TS/TDPL and gTS/GTDPL, which are here proven equivalent in effective recognition power.

Conjunctive grammars are basically context-free grammars with an explicit set intersection operation added to the formalism of rules. This paper presents a cubictime recognition and parsing algorithm for this family of grammars, which is applicable to an arbitrary conjunctive grammar without any initial transformations.

Linear conjunctive grammars are conjunctive grammars in which the body of each conjunct contains no more than a single nonterminal symbol. They can at the same time be thought of as a special case of conjunctive grammars and as a generalization of linear context-free grammars.

We investigate the complexity and expressive power of a spatial logic for reasoning about graphs. This logic was previously introduced by Cardelli, Gardner, and Ghelli, and provides the simplest setting in which to explore such results for spatial logics. We study several forms of the logic: the logic with and without recursion, and with either an exponential or a linear version of the basic composition operator. We study the combined complexity and the expressive power of the four combinations. We prove that, without recursion, the linear and exponential versions of the logic correspond to significant fragments of first-order (FO) and monadic second-order (MSO) logics; the two versions are actually equivalent to FO and MSO on graphs representing strings. However, when the two versions are enriched with-style recursion, their expressive power is sharply increased. Both are able to express PSPACE-complete problems, although their combined complexity and data complexity still belong to PSPACE.

This paper introduces a new family of automata that turns out to be computationally equivalent to linear conjunctive grammars | which are linear context-free grammars extended with an explicit intersection operation.

Whale Calf is a parser generator that uses conjunctive grammars, a generalization of context-free grammars with an explicit intersection operation, as the formalism of specifying the language. All existing parsing algorithms for conjunctive grammars are implemented { namely, the tabular algorithms for grammars in the binary normal form, the tabular algorithm for grammars in the linear normal form, the tabular algorithm for arbitrary grammars, the conjunctive LL, the conjunctive LR, and the algorithm based on simulation of the automata equivalent to linear conjunctive grammars. The generated C++ programs can recognize strings and, if necessary, create parse trees.

The languages generated by linear conjunctive grammars have been recently proved to have a simple automaton characterization. This paper begins the study of the descriptional complexity of this language family by obtaining several results on number of states in these automata.

The Generalized LR parsing algorithm for context-free grammars, introduced by Tomita in 1986, is a polynomial-time implementation of nondeterministic LR parsing that uses graph-structured stack to represent the contents of the nondeterministic parser's pushdown for all possible branches of computation at a single computation step. It has been specifically developed as a solution for practical parsing tasks arising in computational linguistics, and indeed has proved itself to be very suitable for natural language processing.

Systems of equations over sets of natural numbers (or, equivalently, language equations over a one-letter alphabet) of the form Xi = ϕi(X1,..., Xn) (1 � i � n) are considered. Expressions ϕi may contain the operations of union, intersection and pairwise sum A+B = {x+y | x ∈ A, y ∈ B}. A system with an EXPTIME-complete least solution is constructed, and it is established that least solutions of all such systems are in EXPTIME. The general membership problem for these equations is proved to be EXPTIME-complete.

Linear conjunctive grammars have recently been proved computationally equivalent to triangular trellis automata. The relation between these grammars and these automata resembles that between regular expressions and finite automata: while the former are better suited for human use, the latter are considerably easier to implement. This paper studies efficient algorithms for converting a linear conjunctive grammar to an equivalent triangular trellis automaton, and also proposes a number of techniques of reducing the size of these automata.