This paper addresses the problem of defining a formal tool to compare the expressive power of different concurrent constraint languages. We refine the notion of embedding by adding some "reasonable" conditions, suitable for concurrent frameworks. The new notion, called modular embedding, is used to define a preorder among these languages, representing different degrees of expressiveness. We show that this preorder is not trivial (i.e. it does not collapse into one equivalence class) by proving that Flat CP cannot be embedded into Flat GHC, and that Flat GHC cannot be embedded into a language without communication primitives in the guards, while the converses hold. 4 A; C; D; G; M;O;P;R; T : In calligraphic style. ss; ff ; dd: In slanted style. \Sigma; \Gamma; #; oe; ; /; ø; ff. S ; [; "; ;; 2 j=; 6j=; ; 9 +; k; ~ +; ~ k; ! \Gamma! W ; \Gamma! ; ; \Gamma! W ; \Gamma! ; h; i; [[; ]]; d; e ffi; ?; ; 5 All reasonable programming languages are equivalent, since they are Turing...

We analyze the relative expressive power of variants of the indeterminate fair merge operator in the context of static dataflow. We establish that there are three different, provably inequivalent, forms of unbounded indeterminacy. In particular, we show that the well-known fair merge primitive cannot be expressed with just unbounded indeterminacy. Our proofs are based on a simple trace semantics and on identifying properties of the behaviors of networks that are invariant under network composition. The properties we consider in this paper are all generalizations of monotonicity. 1 Introduction The study of indeterminate computing systems is motivated by seeking to understand the theory underlying what is commonly called "distributed systems" programming. In such systems indeterminacy is introduced when one abstracts away from low level hardware or timing details. The subject receives further im- Present Address: School of Computer Science, McGill University, Montreal, PQ, CANADA y...