TY - JOUR

T1 - Communication complexity meets cellular automata

T2 - Necessary conditions for intrinsic universality

AU - Briceño, Raimundo

AU - Rapaport, Ivan

N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature B.V.

PY - 2021/6

Y1 - 2021/6

N2 - A natural way to interpret a cellular automaton (CA) is as a mechanism that computes, in a distributed way, some function f. In other words, from a computer science point of view, CAs can be seen as distributed systems where the cells of the CAs are nodes of a network linked by communication channels. A classic measure of efficiency in such distributed systems is the number of bits exchanged during the computation process. A typical approach is to look for bottlenecks: channels through which the nature of the function f forces the exchange of a significant number of bits. In practice, a widely used way to understand such congestion phenomena is to partition the system into two subsystems and try to find bounds for the number of bits that must pass through the channels that join them. Finding these bounds is the focus of communication complexity theory. Measuring the communication complexity of some problems induced by a CA ϕ turned out to be tremendously useful to give clues regarding the intrinsic universality of ϕ (a CA is said to be intrinsically universal if it is capable of emulating any other). In fact, there exist particular problems P ’s for which the following key property holds: if ϕ is intrinsically universal, then the communication complexity of P (ϕ) must be maximal. In this tutorial, we intend to explain the connections that were found, through a series of papers, between intrinsic universality and communication complexity in CAs.

AB - A natural way to interpret a cellular automaton (CA) is as a mechanism that computes, in a distributed way, some function f. In other words, from a computer science point of view, CAs can be seen as distributed systems where the cells of the CAs are nodes of a network linked by communication channels. A classic measure of efficiency in such distributed systems is the number of bits exchanged during the computation process. A typical approach is to look for bottlenecks: channels through which the nature of the function f forces the exchange of a significant number of bits. In practice, a widely used way to understand such congestion phenomena is to partition the system into two subsystems and try to find bounds for the number of bits that must pass through the channels that join them. Finding these bounds is the focus of communication complexity theory. Measuring the communication complexity of some problems induced by a CA ϕ turned out to be tremendously useful to give clues regarding the intrinsic universality of ϕ (a CA is said to be intrinsically universal if it is capable of emulating any other). In fact, there exist particular problems P ’s for which the following key property holds: if ϕ is intrinsically universal, then the communication complexity of P (ϕ) must be maximal. In this tutorial, we intend to explain the connections that were found, through a series of papers, between intrinsic universality and communication complexity in CAs.

KW - Cellular automata

KW - Communication complexity

KW - Intrinsic universality

UR - http://www.scopus.com/inward/record.url?scp=85107459694&partnerID=8YFLogxK

U2 - 10.1007/s11047-021-09857-z

DO - 10.1007/s11047-021-09857-z

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AN - SCOPUS:85107459694

SN - 1567-7818

VL - 20

SP - 307

EP - 320

JO - Natural Computing

JF - Natural Computing

IS - 2

ER -