Clocked Cubical Type Theory is a new type theory combining the power of guarded recursion with univalence and higher inductive types (HITs). This can be used as metalanguage for synthetic domain in which one solve recursive equations, also negative variable occurrences, use these to construct models reasoning about programming languages. Combining this HITs allows constructors familiar from set...

Motivated by natural language analysis we introduce restarting automata with rewriting. They are acceptors on the one hand, and (special) regulated rewriting systems on the other hand. The computation of a restarting automaton proceeds in cycles: in each cycle, a bounded substring of the input word is rewritten by a shorter string, and the computation restarts on the arising shorter word. We sh...

Exponentiation makes the difference between the bit-size of this line and the number (≪ 2) of particles in the known Universe. The expulsion of exponential time algorithms from Computer Theory in the 60’s broke its umbilical cord from Mathematical Logic. It created a deep gap between deterministic computation and – formerly its unremarkable tools – randomness and non-determinism. Little did we ...

This paper describes the runtime kernel of Paclib, a new system for parallel algebraic computation on shared memory computers. Paclib has been developed as a professional tool for the simple design and eecient implementation of parallel algorithms in computer algebra and related areas. It provides concurrency, shared memory communication , non-determinism, speculative parallelism, streams and a...

The computational operation called synchronization, vital for realizing multi-process systems, is described in terms of geometric (Cli ord) algebras over {-1,0,1}. This provides a two-way bridge between the worlds of computation and quantum mechanics, and casts new light on such matters as quantum non-determinism, mechanism and causality, the explicit structure of particles (including dark matt...

This paper describes the runtime kernel of paclib, a new system for parallel algebraic computation on shared memory computers. paclib has been developed as a professional tool for the simple design and eecient implementation of parallel algorithms in computer algebra and related areas. It provides concurrency, shared memory communication, non-determinism, speculative parallelism, streams and pi...

As modern architectures introduce additional heterogeneity and parallelism, we look for ways to deal with this that do not involve specialising software to every platform. In this paper, we take the Join Calculus, an elegant model for concurrent computation, and show how it can be mapped to an architecture by a Cartesian-product-style construction, thereby making use of the calculus’ inherent n...

This paper presents the foundations of RAPIDS (“Replicated Ada Partitions In Distributed Systems”), an implementation of the Distributed Systems Annex E incorporating the transparent replication of partitions in distributed Ada 95 applications. RAPIDS is a replication manager for semi–active replication based on a piecewise deterministic computation model. It guarantees replica consistency for ...