Mechanized Theory of Event Structures: A Case of Parallel Register Machine

The true concurrency models, and in particular event structures, have been introduced in the 1980s as an alternative to operational interleaving semantics of concurrency, and nowadays they are regaining popularity. Event structures represent the causal dependency and conflict between the individual atomic actions of the system directly. This property leads to a more compact and concise representation of semantics. In this work-in-progress report, we present a theory of event structures mechanized in the COQ proof assistant and demonstrate how it can be applied to define certified executable semantics of a simple parallel register machine with shared memory.

From Turing machines to computer viruses

Self-replication is one of the fundamental aspects of computing where a program or a system may duplicate, evolve and mutate. Our point of view is that Kleene's (second) recursion theorem is essential to understand self-replication mechanisms. An interesting example of self-replication codes is given by computer viruses. This was initially explained in the seminal works of Cohen and of Adleman in the 1980s. In fact, the different variants of recursion theorems provide and explain constructions of self-replicating codes and, as a result, of various classes of malware. None of the results are new from the point of view of computability theory. We now propose a self-modifying register machine as a model of computation in which we can effectively deal with the self-reproduction and in which new offsprings can be activated as independent organisms.

REGISTER MACHINE COMPUTATIONS ON BINARY NUMBERS BY OSCILLATING AND CATALYTIC CHEMICAL REACTIONS MODELLED USING MASS-ACTION KINETICS

Biocomputing emerged as a promising paradigm capable of coping efficiently with challenges of programming decentralized but concerted reaction systems. The chemical programming metaphor subsumes different encoding techniques into molecular or spatial structures in conjunction with artificial reaction networks. Here, a variety of supplementary assumptions like predefined polymeric sequences or availability of inhibiting reactions is frequently used. Inspired by the idea to build chemical computers based on minimal requirements in chemistry from a theoretical perspective, we introduce a pure chemical register machine model operating on binary numbers. The register machine architecture is composed of reaction network motifs acting as fast switching logic gates, oscillators, and self-reproducible bit storage units. The dynamical machine behavior consistently employs mass-action kinetics. Two case studies, calculating the maximum of three natural numbers as well as numerical addition, illustrate the practicability of the design along with dynamical simulations.

A NEW UNIVERSAL CELLULAR AUTOMATON ON THE PENTAGRID

In this paper, we significantly improve a result of the first author, published in an issue of Theoretical Computer Science in 2003. In this paper, the authors showed the existence of a weakly universal cellular automaton on the pentagrid with 22 states. The simulation used a railway circuit which simulates a register machine. In the present paper, using the same simulation tool, we lower the number of states for a weakly universal cellular automaton down to 9.