Minimalist grammars (MGs), formalized by Edward Stabler in 1997 and refined by subsequent work, provide a mathematically rigorous instantiation of the key ideas in Noam Chomsky's Minimalist Program. The Minimalist Program seeks to reduce the syntactic component of grammar to the simplest possible form — ideally to the single structure-building operation Merge, which combines two syntactic objects into a larger one. Minimalist grammars make this vision computationally precise by defining explicit data structures for syntactic features and formal operations for Merge (combining two expressions) and Move (internal merge, displacing a sub-expression).
Merge and Move
In Stabler's formalization, lexical items carry sequences of syntactic features that drive derivation. Features come in two polarities: selectors (which seek arguments) and licensors/licensees (which trigger movement). The Merge operation combines two expressions when one has a selector feature that matches the category feature of the other. The Move operation applies when an expression contains a licensee feature that matches a licensor feature, resulting in displacement of the sub-expression carrying the licensee feature to a higher position.
Merge: combines =X selector with X category
Move: matches +f licensor with -f licensee
Derivation proceeds until all features are checked.
Generative Capacity
A fundamental result in the theory of minimalist grammars is that they are weakly equivalent to multiple context-free grammars (MCFGs) — and thus to several other mildly context-sensitive formalisms including linear context-free rewriting systems (LCFRSs) and set-local multi-component TAGs. This means that despite their derivational, transformational character, minimalist grammars generate exactly the class of mildly context-sensitive languages. This equivalence result, established by Michaelis (2001) and refined by others, provides a bridge between the transformational tradition and the constraint-based/formal language traditions in computational linguistics.
While MGs and MCFGs are weakly equivalent (they generate the same string languages), they differ in strong generative capacity (the structural descriptions they assign). MG derivation trees encode the history of Merge and Move operations, producing structures that correspond to the standard transformational-generative analysis of movement, binding, and control. This makes MGs attractive for linguists who work within the Minimalist Program and wish to maintain familiar structural analyses while gaining formal rigor.
Parsing and Complexity
Minimalist grammars can be parsed in polynomial time. Harkema (2001) showed that MGs can be parsed in O(n^(4k+4)) time, where k is related to the number of movement types, using a CYK-like algorithm. More efficient parsing algorithms have since been developed, bringing MG parsing closer to practical applicability. The complexity results show that despite the dynamic, transformational nature of MG derivations, the computational cost of parsing does not exceed that of other mildly context-sensitive formalisms.
Minimalist grammars have stimulated a rich body of theoretical work on topics including the formal properties of movement types (head movement, remnant movement), the effects of locality constraints on generative capacity, and the relationship between derivational and representational approaches to syntax. They provide a valuable bridge between theoretical linguistics and formal language theory, allowing questions about linguistic universals, learnability, and processing complexity to be stated and investigated with mathematical precision.