Proving Quadratic Derivational Complexities Using Context Dependent Interpretations
نویسندگان
چکیده
In this paper we study context dependent interpretations, a semantic termination method extending interpretations over the natural numbers, introduced by Hofbauer. We present two subclasses of context dependent interpretations and establish tight upper bounds on the induced derivational complexities. In particular we delineate a class of interpretations that induces quadratic derivational complexity. Furthermore, we present an algorithm for mechanically proving termination of rewrite systems with context dependent interpretations. This algorithm has been implemented and we present ample numerical data for the assessment of the viability of the method.
منابع مشابه
Cdiprover3: A Tool for Proving Derivational Complexities of Term Rewriting Systems
This paper describes cdiprover3 a tool for proving termination of term rewrite systems by polynomial interpretations and context dependent interpretations. The methods used by cdiprover3 induce small bounds on the derivational complexity of the considered system. We explain the tool in detail, and give an overview of the employed proof methods.
متن کاملContext Dependent Interpretations
Context-dependent interpretations are a termination proof method developed by Hofbauer in 2001. They extend the interpretations into F-algebras by introducing an additional parameter to the interpretation functions. The additional parameter is changed by the context of the evaluated subterm, thus giving rise to the name “context-dependent interpretations”. They were designed to give good upper ...
متن کاملComplexity Analysis of Term Rewriting Based on Matrix and Context Dependent Interpretations
For a given (terminating) term rewriting system one can often estimate its derivational complexity indirectly by looking at the proof method that established termination. In this spirit we investigate two instances of the interpretation method: matrix interpretations and context dependent interpretations. We introduce a subclass of matrix interpretations, denoted as triangular matrix interpreta...
متن کاملAn Epistemological Study of the Verse Tathir
The verse Tathir is regarded as one of the central verses in proving the infallibility of the Prophet and his future generation`s properties that have long been debated among the Fariqain commentators. The Sunni commentators, without any reasonable proof and only based on the context and etymology of the word al-bait, the house, have viewed all members of Quraysh in the Prophet's House, and in ...
متن کاملBeyond Peano Arithmetic - Automatically Proving Termination of the Goodstein Sequence
Kirby and Paris (1982) proved in a celebrated paper that a theorem of Goodstein (1944) cannot be established in Peano (1889) arithmetic. We present an encoding of Goodstein’s theorem as a termination problem of a finite rewrite system. Using a novel implementation of ordinal interpretations, we are able to automatically prove termination of this system, resulting in the first automatic terminat...
متن کامل