Related papers: Deciding and Interpolating Algebraic Data Types by…
In this work, we address question answering (QA) over a hybrid of tabular and textual data that are very common content on the Web (e.g. SEC filings), where discrete reasoning capabilities are often required. Recently, large language models…
Large Language Models (LLMs) are increasingly being used for interactive decision-making tasks requiring planning and adapting to the environment. Recent works employ LLMs-as-agents in broadly two ways: iteratively determining the next…
Weighted Logic is a powerful tool for the specification of calculations over semirings that depend on qualitative information. Using a novel combination of Weighted Logic and Here-and-There (HT) Logic, in which this dependence is based on…
Converse PDL is the extension of propositional dynamic logic with a converse operation on programs. Our main result states that Converse PDL enjoys the (local) Craig Interpolation Property, with respect to both atomic programs and…
Accelerated degradation testing (ADT) is one of the major approaches in reliability engineering which allows accurate estimation of reliability characteristics of highly reliable systems within a relatively short time. The testing data are…
While programmers know that the low-level memory representation of data structures can have significant effects on performance, compiler support to optimize the layout of those structures is an under-explored field. Prior work has optimized…
We introduce LAM, a subsystem of IMALL2 with restricted additive rules able to manage duplication linearly, called linear additive rules. LAM is presented as the type assignment system for a calculus endowed with copy constructors, which…
Humans can develop new theorems to explore broader and more complex mathematical results. While current generative language models (LMs) have achieved significant improvement in automatically proving theorems, their ability to generate new…
In this paper, we propose an analysis mechanism based structured Analysis Discriminative Dictionary Learning (ADDL) framework. ADDL seamlessly integrates the analysis discriminative dictionary learning, analysis representation and analysis…
Data replication is used in distributed systems to maintain up-to-date copies of shared data across multiple computers in a network. However, despite decades of research, algorithms for achieving consistency in replicated systems are still…
Solving constraints involving inductive (aka recursive) definitions is challenging. State-of-the-art SMT/CHC solvers and first-order logic provers provide only limited support for solving such constraints, especially when they involve,…
A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…
Large Language Models (LLMs) have been achieving competent performance on a wide range of downstream tasks, yet existing work shows that inference on structured data is challenging for LLMs. This is because LLMs need to either understand…
In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof…
Automated mathematical reasoning is a challenging problem that requires an agent to learn algebraic patterns that contain long-range dependencies. Two particular tasks that test this type of reasoning are (1) mathematical equation…
Large Language Models (LLMs) gain substantial reasoning and decision-making capabilities from thought structures. However, existing methods such as Tree of Thought and Retrieval Augmented Thoughts often fall short in complex tasks due to…
A self-learning algebraic multigrid method for dominant and minimal singular triplets and eigenpairs is described. The method consists of two multilevel phases. In the first, multiplicative phase (setup phase), tentative singular triplets…
Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…
We develop foundations for computing Craig interpolants and similar intermediates of two given formulas with first-order theorem provers that construct clausal tableaux. Provers that can be understood in this way include efficient…
Data replication is crucial for enabling fault tolerance and uniform low latency in modern decentralized applications. Replicated Data Types (RDTs) have emerged as a principled approach for developing replicated implementations of basic…