Embedded pushdown automaton

An embedded pushdown automaton or EPDA is a computational model for parsing languages generated by tree-adjoining grammars (TAGs). It is similar to the context-free grammar-parsing pushdown automaton, but instead of using a plain stack to store symbols, it has a stack of iterated stacks that store symbols, giving TAGs a generative capacity between context-free and context-sensitive grammars, or a subset of mildly context-sensitive grammars. Embedded pushdown automata should not be confused with nested stack automata which have more computational power. EPDAs were first described by K. Vijay-Shanker in his 1988 doctoral thesis. They have since been applied to more complete descriptions of classes of mildly context-sensitive grammars and have had important roles in refining the Chomsky hierarchy. Various subgrammars, such as the linear indexed grammar, can thus be defined. While natural languages have traditionally been analyzed using context-free grammars (see transformational-generative grammar and computational linguistics), this model does not work well for languages with crossed dependencies, such as Dutch, situations for which an EPDA is well suited. A detailed linguistic analysis is available in Joshi, Schabes (1997). An EPDA is a finite state machine with a set of stacks that can be themselves accessed through the embedded stack. Each stack contains elements of the stack alphabet , and so we define an element of a stack by , where the star is the Kleene closure of the alphabet. Each stack can then be defined in terms of its elements, so we denote the th stack in the automaton using a double-dagger symbol: , where would be the next accessible symbol in the stack. The embedded stack of stacks can thus be denoted by . We define an EPDA by the septuple (7-tuple) where is a finite set of states; is the finite set of the input alphabet; is the finite stack alphabet; is the start state; is the set of final states; is the initial stack symbol is the transition function, where are finite subsets of .