Related papers: Left-Linear Rewriting in Adhesive Categories
Discrete structures are currently second-class in differentiable programming. Since functions over discrete structures lack overt derivatives, differentiable programs do not differentiate through them and limit where they can be used. For…
Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…
This paper focuses on automated synthesis of divide-and-conquer parallelism, which is a common parallel programming skeleton supported by many cross-platform multithreaded libraries. The challenges of producing (manually or automatically) a…
Constraint Handling Rules (CHR) is a declarative rule-based formalism and language. Concurrency is inherent as rules can be applied to subsets of constraints in parallel. Parallel implementations of CHR, be it in software, be it in…
This paper is about output-feedback control problems for general linear systems in the presence of given state-, control-, disturbance-, and measurement error constraints. Because the traditional separation theorem in stochastic control is…
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…
In this paper we show how string rewriting methods can be applied to give a new method of computing double cosets. Previous methods for double cosets were enumerative and thus restricted to finite examples. Our rewriting methods do not…
Data replication is essential to ensure reliability, availability and fault-tolerance of massive distributed applications over large scale systems such as the Internet. However, these systems are prone to partitioning, which by Brewer's CAP…
The concept of a system has proliferated through natural and social sciences. While myriad theories of systems exist, there is no mathematical general theory of systems. In this thesis, we take a first step towards formulating such a…
Recent advances in Large Language Models(LLMs) have enabled strong performance in long-form writing, but current training paradigms remain limited: Supervised Fine-Tuning (SFT) remains constrained by data saturation and performance…
Taking advantage of a recently discovered associativity property of rule compositions, we extend the classical concurrency theory for rewriting systems over adhesive categories. We introduce the notion of tracelets, which are defined as…
We revisit test-time scaling for language model reasoning and ask a fundamental question: at equal token budget and compute, is it better to run multiple independent chains in parallel, or to run fewer chains that iteratively refine through…
To refine formal methods for concurrent systems, there are several ways of enriching classical operational semantics of process calculi. One can enable the auditing and undoing of past synchronisations thanks to communication keys, thus…
General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language…
We introduce a general theory of quantitative and metric rewriting systems, namely systems with a rewriting relation enriched over quantales modelling abstract quantities. We develop theories of abstract and term-based systems, refining…
In this paper we use the decreasing diagrams technique to show that a left-linear term rewrite system R is confluent if all its critical pairs are joinable and the critical pair steps are relatively terminating with respect to R. We further…
Implementing a concurrent data structure typically begins with defining its sequential specification. However, when used \emph{as is}, a nontrivial sequential data structure, such as a linked list, a search tree, or a hash table, may expose…
Locks are a standard mechanism for synchronizing concurrent threads. The standard lock set construction assumes that critical sections are confined to a single thread, and therefore only accounts for locks acquired within that thread.…
Repeated recursion unfolding is a new approach that repeatedly unfolds a recursion with itself and simplifies it while keeping all unfolded rules. Each unfolding doubles the number of recursive steps covered. This reduces the number of…
Computer science is also an experimental science. This is particularly the case for parallel computing, which is in a total state of flux, and where experiments are necessary to substantiate, complement, and challenge theoretical modeling…