Related papers: Separating LREC from LFP

We propose a formal model of distributed computing based on register automata that captures a broad class of synchronous network algorithms. The local memory of each process is represented by a finite-state controller and a fixed number of…

To comprehensively evaluate the mathematical reasoning capabilities of Large Language Models (LLMs), researchers have introduced abundant mathematical reasoning datasets. However, most existing datasets primarily focus on linear reasoning,…

A new approach to solving a large class of factorable nonlinear programming (NLP) problems to global optimality is presented in this paper. Unlike the traditional strategy of partitioning the decision-variable space employed in many…

We consider the sublanguages of Plotkin's PCF obtained by imposing some bound k on the levels of types for which fixed point operators are admitted. We show that these languages form a strict hierarchy, in the sense that a fixed point…

The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. Such logic formally extends logic programming, abductive logic programming and datalog, and thus formalizes…

Linear logic Concurrent Constraint programming (LCC) is an extension of concurrent constraint programming (CC) where the constraint system is based on Girard's linear logic instead of the classical logic. In this paper we address the…

We introduce PHFL, a probabilistic extension of higher-order fixpoint logic, which can also be regarded as a higher-order extension of probabilistic temporal logics such as PCTL and the $\mu^p$-calculus. We show that PHFL is strictly more…

First-order logic is known to have limited expressive power over finite structures. It enjoys in particular the locality property, which states that first-order formulae cannot have a global view of a structure. This limitation ensures on…

Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and…

This paper defines a new proof- and category-theoretic framework for classical linear logic that separates reasoning into one linear regime and two persistent regimes corresponding to ! and ?. The resulting linear/producer/consumer (LPC)…

In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…

A system of linear dependent types for the lambda calculus with full higher-order recursion, called dlPCF, is introduced and proved sound and relatively complete. Completeness holds in a strong sense: dlPCF is not only able to precisely…

Large Language Model agents often retrieve context from knowledge bases that lack structural consistency with the agent's current reasoning state, leading to incoherent reasoning chains. We introduce Path-Constrained Retrieval (PCR), a…

We study Boolean classification problems over relational background structures in the logical framework introduced by Grohe and Tur\'an (TOCS 2004). It is known (Grohe and Ritzert, LICS 2017) that classifiers definable in first-order logic…

Large language models achieve strong reasoning performance, but inference strategies such as Self-Consistency (SC) are computationally expensive, as they fully expand all reasoning traces. We introduce PoLR (Path of Least Resistance), the…

Complexity and decidability of logics is a major research area involving a huge range of different logical systems. This calls for a unified and systematic approach for the field. We introduce a research program based on an algebraic…

Recent research revealed the existence of gaps in the complexity landscape of locally checkable labeling (LCL) problems in the LOCAL model of distributed computing. For example, the deterministic round complexity of any LCL problem on…

The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…

Linear Genetic Programming (LGP) is a powerful technique that allows for a variety of problems to be solved using a linear representation of programs. However, there still exists some limitations to the technique, such as the need for…

LLMs demonstrate strong performance on code benchmarks, yet consistent reasoning across forward and backward execution remains elusive. We present RoundTripCodeEval (RTCE), a benchmark of four code execution reasoning tasks that evaluates…