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Generalized finite automata theory with an application to a decision problem of second-order logic
TLDR
Finite algebras take the place of finite automata in second-order logic, and a generalization of Kleene's regularity theory is developed. Expand
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Initial Algebra Semantics and Continuous Algebras
TLDR
An overview of initial algebra semantics which permits unified algebraic treatment of iterative and recursive semantic features in the same framework as basic operations. Expand
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Algebraic Automata and Context-Free Sets
TLDR
The concepts of “equational≓ and “recognizable≓ are defined for sets of elements of an arbitrary abstract algebra. Expand
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Automata in General Algebras
TLDR
The study of automata and of context-free languages usually deals with monoids or semigroups. Expand
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Realization of Events by Logical Nets
TLDR
In Representation of Events in Nerve Nets and Finite Automata [3], S. C. Kleene obtains a number of interesting results. Expand
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P-varieties - a signature independent characterization of varieties of ordered algebras
Abstract This paper is concerned mainly with classes (categories) of ordered algebras which in some signature are axiomatizable by a set of inequations between terms (‘varieties’ of ordered algebras)Expand
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Data type specification: Parameterization and the power of specification techniques
TLDR
This paper extends our earlier work on abstract data types by providing an algebraic treatment of parametrized data types (e.g., sets-of-(), stacks-of, etc. Expand
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Data Type Specification: Parameterization and the Power of Specification Techniques
TLDR
We investigate the "hidden function" problem (the need to include operat ions in specifications which we want to be hidden from the user); we prove that condit ional specifications are inherently more powerful than equational specifications; we compare the power of the algebraic approach taken here with the categorical approach of Lehman and Smyth . Expand
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More on Advice on Structuring Compilers and Proving Them Correct
TLDR
This paper can be seen as the fourth in the sequence: McCarthy and Painter (1967), Burstall and Landin (1970) and Morris (1973). Expand
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