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.

Minimalist Grammars are a rigorous formalization of the sort of grammars proposed in the linguistic framework of Chomsky's Minimalist Program. One notable property of Minimalist Grammars is that they allow constituents to move during the derivation of a sentence, thus creating discontinuous constituents.

this article appeared in Glot, the main issue agitating researchers in model theoretic syntax was the problem of the context-free barrier. We have seen that the hierarchy of logics collapses, when applied to trees, at the border of the tree languages strongly generated by context free (string) grammars, in the sense that distinctions between the different tree logics reduce to apparently superficial distinctions in how much memory allocation is hidden in the logic. The problem which researchers set themselves was not just breaking the context free barrier but remaining decidable in the process. This is a very difficult problem, and it must be admitted right off that it is somewhat artificial in that there is no a priori reason to suppose that natural languages can be described in a decidable logic. The arguments on either side are something like the following. First, the rather slight increases in computational complexity required to get the "mildly context sensitive" languages do suggest that this might be possible. The hunch here would be that the qualities that characterize the mildly context sensitive languages (polynomial parsability, constant growth property) as being like the context-free languages are going to turn out to be reflections of decidability. The problems must not be underestimated, however! It is well known that the monadic second order logic of trees is one of the most powerful decidable logics known. It seems unlikely that any primitive relations can be added to the repertoire of tree description primitives that we have already seen, without making the logic undecidable. Many attempts have been made within logic and all have failed. So it is equally tempting to conjecture that the context-free boundary coincides in some deep sense with the bounda...

This paper examines issues in parsing architecture for a left-to-right implementation of the probe-goal Case agreement model, a theory in the Minimalist Program (MP). Computation from a parsing perspective imposes special constraints. For example, in left-to-right parsing, the assembly of phrase structure must proceed through elementary tree composition, rather than using using the generative operations merge and move directly. On-line processing also poses challenges for the incremental computation of probe/goal relations. We describe an implemented parser that computes these relations and assembles phrase structure, whilst respecting the incremental and left-to-right nature of parsing. The model employs two novel mechanisms, a Move and a Probe box, to implement e#cient parsing, without "lookback" or unnecessary search of the derivational history.