Related papers: Truly Concurrent Process Algebra Is Reversible
Using formal tools in computer science to describe games is an interesting problem. We give games, exactly two person games, an axiomatic foundation based on the process algebra ACP (Algebra of Communicating Process). A fresh operator…
We study a class of functional problems reducible to computing $f^{(n)}(x)$ for inputs $n$ and $x$, where $f$ is a polynomial-time bijection. As we prove, the definition is robust against variations in the type of reduction used in its…
We present an extended version of max-plus algebra which includes the inverse operator of "max". This algebra enables us to ultra-discretize the system including subtractions and obtain new ultra-discrete equations. The known ultra-discrete…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…
Given a simple recursive function, we show how to extract from it a reversible and an classical iterative part. Those parts can synchronously cooperate under a Producer/Consumer pattern in order to implement the original recursive function.…
Causal-consistent reversibility is the reference notion of reversibility for concurrency. We introduce a modular framework for defining causal-consistent reversible extensions of concurrent models and languages. We show how our framework…
The training algorithms for AI systems all introduce far-from-equilibrium dynamical processes, and understanding the irreversibility of these algorithms is a fundamental step towards understanding the learning dynamics of modern AI systems.…
We introduce and characterize a particularly tractable class of unital type 1 C*-algebras with bounded dimension of irreducible representations. Algebras in this class are called recursive subhomogeneous algebras, and they have an inductive…
This paper presents an algebraic theory of instruction sequences with instructions for a random access machine (RAM) as basic instructions, the behaviours produced by the instruction sequences concerned under execution, and the interaction…
For readers already familiar with Partial Information Decomposition (PID), we show that PID's definition of synergy enables quantifying at least four different notions of irreducibility. First, we show four common notions of "parts" give…
This book offers an introduction to vertex algebra based on a new approach. The new approach says that a vertex algebra is an associative algebra such that the underlying Lie algebra is a vertex Lie algebra. In particular, vertex algebras…
Reproducibility of modeling is a problem that exists for any machine learning practitioner, whether in industry or academia. The consequences of an irreproducible model can include significant financial costs, lost time, and even loss of…
We study the Reverse algorithm, a multidimensional continued fraction algorithm, which is not unimodular. We show that the Reverse algorithm is ergodic and, by proving that its second Lyapunov exponent is negative, that it is a.e.…
In this work, we incorporate reversibility into structured communication-based programming, to allow parties of a session to automatically undo, in a rollback fashion, the effect of previously executed interactions. This permits taking…
This paper concerns the relation between imperative process algebra and rely/guarantee logic. An imperative process algebra is complemented by a rely/guarantee logic that can be used to reason about how data change in the course of a…
The asynchronous computability theorem (ACT) uses concepts from combinatorial topology to characterize which tasks have wait-free solutions in read-write memory. A task can be expressed as a relation between two chromatic simplicial…
In a previous paper, we presented several extensions of ACP with conditional expressions, including one with a retrospection operator on conditions to allow for looking back on conditions under which preceding actions have been performed.…
This paper introduces a new structure of commutative semiring, generalizing the tropical semiring, and having an arithmetic that modifies the standard tropical operations, i.e. summation and maximum. Although our framework is combinatorial,…
Fully automatic worst-case complexity analysis has a number of applications in computer-assisted program manipulation. A classical and powerful approach to complexity analysis consists in formally deriving, from the program syntax, a set of…