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In this paper we present a proof of a mathematical version of the strongcosmic censor conjecture attributed to Geroch-Horowitz and Penrose butformulated explicitly by Wald. The proof is based on the existence offuture-inextendible causal curves in causal pasts of events on the futureCauchy horizon in a non-globally hyperbolic space-time. By examining explicitnon-globally hyperbolic space-times we find that in case of several physicallyrelevant solutions these future-inextendible curves have in fact infinitelength. This way we recognize a close relationship between asymptotically flator anti-de Sitter, physically relevant extendible space-times and the so-calledMalament-Hogarth space-times which play a central role in recent investigationsin the theory of "gravitational computers". This motivates us to exhibit a moresharp, more geometric formulation of the strong cosmic censor conjecture,namely "all physically relevant, asymptotically flat or anti-de Sitter butnon-globally hyperbolic space-times are Malament-Hogarth ones".  Our observations may indicate a natural but hidden connection between thestrong cosmic censorship scenario and the Church-Turing thesis revealing anunexpected conceptual depth beneath both conjectures.

A proof of the Geroch-Horowitz-Penrose formulation of the strong cosmic censor conjecture motivated by computability theory