Sequentialization and Procedural Complexity in Automata Networks

Florian Bridoux (1)

1 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)

In this article we consider finite automata networks (ANs) with two kinds of update schedules: the parallel one (all automata are updated all together) and the sequential ones (the automata are updated periodically one at a time according to a total order w). The cost of sequentialization of a given AN h is the number of additional automata required to simulate h by a sequential AN with the same alphabet. We construct, for any n and q, an AN h of size n and alphabet size q whose cost of sequentialization is at least n/3. We also show that, if q ≥ 4, we can find one whose cost is at least n/2 − log q (n). We prove that n/2 + log q (n/2 + 1) is an upper bound for the cost of sequentialization of any AN h of size n and alphabet size q. Finally, we exhibit the exact relation between the cost of sequentialization of h and its procedural complexity with unlimited memory and prove that its cost of sequentialization is less than or equal to the pathwidth of its interaction graph.

Mots clés: intrinsic simulation; parallel update schedule; sequential update schedules; procedural complexity; Automata networks

Domaines: Mathématique discrète [cs.DM]

Florian Bridoux. Sequentialization and Procedural Complexity in Automata Networks. MFCS2018, Aug 2018, Liverpool, France. ⟨hal-01718527⟩