Tree adjunct grammars

A common tool for proving the termination of programs is the well-founded set, a set ordered in such a way as to admit no infinite descending sequences. The basic approach is to find a termination function that maps the values of the program variables into some well-founded set, such that the value of the termination function is repeatedly reduced throughout the computation. All too often, the termination functions required are difficult to find and are of a complexity out of proportion to the program under consideration.Multisets (bags) over a given well-founded set S are sets that admit multiple occurrences of elements taken from S. The given ordering on S induces an ordering on the finite multisets over S. This multiset ordering is shown to be well-founded. The multiset ordering enables the use of relatively simple and intuitive termination functions in otherwise difficult termination proofs. In particular, the multiset ordering is used to prove the termination of production systems, programs defined in terms of sets of rewriting rules.

/pdf/proving-termination-with-multiset-orderings-3k1pab9m41.pdf

Proving termination with multiset orderings

An algebraic semantics approach to the effective resolution of type equations

From the Publisher:
Early formal specifications of natural language syntax were quite closely connected to the notion of abstract machines for computing them. More recently, this approach has been superseded by one in which languages are specified in terms of systems of constraints on the structure of their sentences. This book presents a natural and quite general means of expressing constraints on the structure of trees and shows that the languages that can be specified by systems of such constraints are exactly those computable by a particular standard class of abstract machines.

A descriptive approach to language-theoretic complexity

We define topdown pushdown tree automata (PDTA's) which extend the usual string pushdown automata by allowing trees instead of strings in both the input and the stack. We prove that PDTA's recognize the class of context-free tree languages. (Quasi)realtime and deterministic PDTA's accept the classes of Greibach and deterministic tree languages, respectively. Finally, PDTA's are shown to be equivalent to restricted PDTA's, whose stack is linear: this both yields a more operational way of recognizing context-free tree languages and connects them with the class of indexed languages.

/pdf/pushdown-tree-automata-1jc5s1ojnz.pdf

Pushdown tree automata

Explicit Definitions and Linguistic Dominoes

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Explicit Definitions and Linguistic Dominoes