Temporal Causal Models as a Model of Computation

TL;DR

This paper demonstrates that Temporal Structural Equation Models (TSEMs) can encode computational models like Turing machines, establishing a link between causal reasoning and classical computation theory.

Contribution

It proves that TSEMs are Turing complete and can encode Linear Bounded Automata, connecting causal models with formal models of computation.

Findings

TSEMs can encode Linear Bounded Automata.

TSEMs with countably many variables are Turing complete.

Establishes a formal link between causal reasoning and computation theory.

Abstract

Causal models, also known as Structural Equation Models (SEM), are a well-known formalism for representing and reasoning about causal dependencies between events. In this paper, we show that Temporal SEMs (TSEMs), which extend SEMs to support causal reasoning in temporal settings, can be interpreted as a model of computation. We prove that TSEMs can encode Linear Bounded Automata, and thus causal settings representable in context sensitive languages. We also prove that TSEMs with countably many variables are Turing complete. These results establish a formal connection between causal reasoning and classical models of computation, enabling the integration of counterfactual reasoning techniques from causal inference into the theory of computation.