The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Stepwise Specification and Implementation of Abstract Data Types
Proceedings of the Fifth Colloquium on Automata, Languages and Programming
Algebraic Implementation of Abstract Data Types: Concept, Syntax, Semantics and Correctness
Proceedings of the 7th Colloquium on Automata, Languages and Programming
Parameterized Data Types in Algebraic Specification Languages (Short Version)
Proceedings of the 7th Colloquium on Automata, Languages and Programming
Complexity of finitely presented algebras
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Data type specification: Parameterization and the power of specification techniques
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Straight-line program length as a parameter for complexity measures
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Abstract data types and the development of data structures
Proceedings of the 1976 conference on Data : Abstraction, definition and structure
Data Types
Algebraic implementation of abstract data types: an announcement
ACM SIGACT News
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The aim of this paper is to study implementations of abstract data types and their complexity within the framework of algebraic specifications. An implementation of an abstract data type ADTO by an abstract data type ADT1 is defined on a syntactical and on a semantical level where data and operations of ADTO are simulated by those of ADT1. In order to investigate complexity of implemented operations and to compair different implementations we axiomatically introduce complexity measures for the operations in ADTO with respect to a given implementation of ADTO by ADT1. A most natural interesting class of complexity measures which satisfy our axioms is compatible with time complexity of Turing Machines. This is shown by specification and implementation of timebounded Turing Machines within our algebraic framework and the simulation of a general nondeterministic interpreter for algebraic implementations by a nondeterministic Turing Machine. This relationship allows to show the existence of solutions and of upper and lower bounds for the complexity of a broad class of implementation problems in our sense. A corollary shows that there are algebraic specifications for all those recursive functions which are bounded in time by algebraically specifyable functions. Since the complexity measure for ADTO-operations in a given implementation IMPL1 of ADTO by ADT1 in general depends on the complexity of the ADT1-operations it is possible to substitute the complexity of the ADT1-operations which may be obtained from an implementation IMPL2 of ADT1 by ADT2. On the other hand the composite implementation IMPL3 of ADTO by ADT2 can be constructed and it is shown that the composite complexity of IMPL3 is less or equal to the substituted complexity considered above provided that some natural consistency conditions are satisfied.