On the parallel computation thesis

Abstract

We develop a generic programming language for parallel algorithms, one that works for all data structures and control structures. We show that any parallel algorithm satisfying intuitively-appealing postulates can be modeled by a collection of cells, each of which is an abstract state machine, augmented with the ability to spawn new cells. The cells all run the same algorithm and communicate via a shared global memory. Using a formal definition of what makes such an algorithm effective, we prove the validity of the Parallel Computation Thesis, according to which all reasonable parallel models of computation have roughly equivalent running times. La filosofia e scritta in questo grandissimo libro che continuamente ci sta aperto innanzi a gli occhi (io dico l’universo) ma non si puo intender se prima non s’ impara a intender la lingua e conoscere i caratteri ne’ quali e scritto. Egli e scritto in lingua matematica e i caratteri sono triangoli, cerchi, ed altre figure geometriche senza i quali mezi e impossibile a intenderne umanamente parola; senza questi e un aggirarsi vanamente per un oscuro laberinto. —Galileo Galilei (Il Saggiatore) This work was carried out in partial fulfillment of the requirements for the Ph.D. degree [22] of the second author. The first author’s research benefitted from a fellowship at the Paris Institute for Advanced Studies (France), with the financial support of the French state, managed by the French National Research Agency’s “Investissements d’avenir” program (ANR11-LABX-0027-01 Labex RFIEA+). A portion of this article was presented in a talk entitled, “Generic Parallel Algorithms,” at Computability in Europe (CiE) 2014 [16]. “Philosophy is written in this grand book, the universe, which stands continually open