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We describe a novel machine model of computation, and prove that this model is capable of performing calculations beyond the capability of the standard Turing machine model. In particular, we demonstrate the ability of our model to solve the Halting problem for Turing machines. We discuss the issues involved in implementing the model as a physical device, and offer some tentative suggestions.

Logicians at the Rényi Mathematical Institute in Budapest have spent several years developing versions of relativity theory (special, general, and other variants) based wholly on first-order logic, and have argued in favour of the physical decidability, via exploitation of cosmological phenomena, of formally unsolvable questions such as the Halting Problem and the consistency of set theory. As part of a joint project, researchers at Sheffield have recently started generating rigorous machine-verified versions of the Hungarian proofs, so as to demonstrate the soundness of their work. In this paper, we explain the background to the project and demonstrate a first-order proof in Isabelle/HOL of the theorem "no inertial observer can travel faster than light". This approach to physical theories and physical computability has several pay-offs, because the precision with which physical theories need to be formalised within automated proof systems forces us to recognise subtly hidden assumptions.

Abstract. P systems are the computational models introduced in the context of membrane computing, a computational paradigm within the more general area of unconventional computing. Kernel P (kP) systems are defined to unify the specification of different variants of P systems, motivated by challenging theoretical aspects and the need to model different problems. kP systems are supported by a software framework, called kPWorkbench, which integrates a set of related simulation and verification methodologies and tools. In this paper, we present an extension to kPWorkbench with a new model checking framework supporting the formal verification of kP system models. This framework supports both LTL and CTL properties. To make the property specification an easier task, we propose a property language, composed of natural language statements. We demonstrate our proposed methodology with an example.