Lower bounds for prams over Z

Luc Pellissier (1, 2) , Thomas Seiller (3, 4)

1 X - École polytechnique
2 PARTOUT - Automatisation et ReprésenTation: fOndation du calcUl et de la déducTion
3 CNRS - Centre National de la Recherche Scientifique
4 LIPN - Laboratoire d'Informatique de Paris-Nord

This paper presents a new abstract method for proving lower bounds in computational complexity. Based on the notion of topological entropy for dynamical systems, the method captures four previous lower bounds results from the literature in algebraic complexity. Among these results lies Mulmuley's proof that "prams without bit operations" do not compute the maxflow problem in polylogarithmic time, which was the best known lower bounds in the quest for a proof that NC = Ptime. Inspired from a refinement of Steele and Yao's lower bounds, due to Ben-Or, we strengthen Mulmuley's result to a larger class of machines, showing that prams over integer do not compute maxflow in polylogarithmic time.

Domaines: Complexité [cs.CC]; Logique en informatique [cs.LO]; Géométrie algébrique [math.AG]; Systèmes dynamiques [math.DS]; Calcul parallèle, distribué et partagé [cs.DC]; Théorie et langage formel [cs.FL]

Luc Pellissier, Thomas Seiller. Lower bounds for prams over Z. 2020. ⟨hal-02487667v1⟩