相关论文: A Coding Theoretic Study on MLL proof nets

We approach the problem of linear network coding for multicast networks from different perspectives. We introduce the notion of the coding points of a network, which are edges of the network where messages combine and coding occurs. We give…

Linear logic has provided new perspectives on proof-theory, denotational semantics and the study of programming languages. One of its main successes are proof-nets, canonical representations of proofs that lie at the intersection between…

A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…

When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted…

In the first part of this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the well-known theory of unit-free multiplicative proof nets. A linking is no longer a set…

Coding, which targets compressing and reconstructing data, and intelligence, often regarded at an abstract computational level as being centered around model learning and prediction, interweave recently to give birth to a series of…

Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…

Error-correction codes are central for fault-tolerant information processing. Here we develop a rigorous framework to describe various coding models based on quantum resource theory of superchannels. We find, by treating codings as…

Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…

Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…

The two major systems of formal verification are model checking and algebraic model-based testing. Model checking is based on some form of temporal logic such as linear temporal logic (LTL) or computation tree logic (CTL). One powerful and…

This paper establishes a bridge between linear logic and mainstream graph theory, building on previous work by Retor\'e (2003). We show that the problem of correctness for MLL+Mix proof nets is equivalent to the problem of uniqueness of a…

Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…

We provide here a proof theoretic account of constraint programming that attempts to capture the essential ingredients of this programming style. We exemplify it by presenting proof rules for linear constraints over interval domains, and…

This paper describes a procedure that system developers can follow to translate typical mathematical representations of linearized control systems into logic theories. These theories are then used to verify system requirements and find…

Network coding is studied when an adversary controls a subset of nodes in the network of limited quantity but unknown location. This problem is shown to be more difficult than when the adversary controls a given number of edges in the…

Proof equivalence in a logic is the problem of deciding whether two proofs are equivalent modulo a set of permutation of rules that reflects the commutative conversions of its cut-elimination procedure. As such, it is related to the…

Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…

We abstract the essential aspects of network-error detecting and correcting codes to arrive at the definitions of matroidal error detecting networks and matroidal error correcting networks. An acyclic network (with arbitrary sink demands)…

Understanding a program's runtime reasoning behavior, meaning how intermediate states and control flows lead to final execution results, is essential for reliable code generation, debugging, and automated reasoning. Although large language…