Spacetime computing: towards algorithmic causal sets with special-relativistic properties

Spacetime computing is undoubtedly one of the most ambitious and less explored forms of unconventional computing. Totally unconventional is the medium on which the computation is expected to take place - the elusive texture of physical spacetime - and unprecedentedly wide its scope, since the emergent properties of these computations are expected to ultimately reproduce everything we observe in nature. First we discuss the distinguishing features of this peculiar form of unconventional computing, and survey a few pioneering approaches. Then we illustrate some novel ideas and experiments that attempt to establish stronger connections with advances in quantum gravity and the physics of spacetime. We discuss techniques for building algorithmic causal sets - our proposed deterministic counterpart of the stochastic structures adopted in the Causal Set programme for discrete spacetime modeling - and investigate, in particular, the extent to which they can reflect an essential feature of continuous spacetime: Lorentz invariance.