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Separating concurrent languages with categories of language embeddings
 In Proceedings of the 23 rd Annual ACM Symposium on Theory of Computing
, 1991
"... Concurrent programming enjoys a proliferation of languages but suffers from the lack of a general method of language comparison. In particular, concurrent (as well as sequential) programming languages cannot be usefully distinguished based on complexitytheoretic considerations, since most of them ..."
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Concurrent programming enjoys a proliferation of languages but suffers from the lack of a general method of language comparison. In particular, concurrent (as well as sequential) programming languages cannot be usefully distinguished based on complexitytheoretic considerations, since most of them are Turingcomplete. Nevertheless, differences between programming languages matter, else we would not have invented so many of them. We develop a general method for comparing concurrent programming languages based on their algebraic (structural) complexity, and, using this method, achieve separation results among many wellknown concurrent languages. The method is not restricted to concurrent languages. It can be used to compare the algebraic complexity of abstract machine models, other families of programming languages, logics, and, more generaly, any family of languages with some syntactic operations and a notion of semantic equivalence. The method can also be used to compare the algebraic complexity of families of operations wit hin a language or across languages. We note that using the method we were able to compare languages and computational models that do not have a common semantic basis.
On the Structural Simplicity of Machines and Languages
, 1993
"... We employ an algebraic method for comparing the structural simplicity of families of abstract machines. We associate with each family of machines a firstorder structure that includes machines as objects, composition operations, which construct larger machines from smaller ones, as functions, and a ..."
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We employ an algebraic method for comparing the structural simplicity of families of abstract machines. We associate with each family of machines a firstorder structure that includes machines as objects, composition operations, which construct larger machines from smaller ones, as functions, and a set of semantic relations. We then compare families of machines by studying the existence of homomorphisms between the associated structures. Given families of machines L, L 0 with associated structures S, S 0 , we say that L is simpler than L 0 if there is a homomorphism of S into S 0 , but not vice versa. We show that across several abstract machine models  finite automata, Turing machines, and logic programs  deterministic machines are simpler than nondeterministic machines and nondeterministic machines are simpler than alternating machines. Our results cross computational complexity boundaries. We show that for Turing machines, finite automata and logic programs every non...