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Typically, machine learning systems solve new tasks by training on thousands of examples. In contrast, humans can solve new tasks by reading some instructions, with perhaps an example or two. To take a step toward closing this gap, we…
This paper describes a large set of related theorem proving problems obtained by translating theorems from the HOL4 standard library into multiple logical formalisms. The formalisms are in higher-order logic (with and without type…
Reachability and LTL model-checking problems for flat counter systems are known to be decidable but whereas the reachability problem can be shown in NP, the best known complexity upper bound for the latter problem is made of a tower of…
Recursive Neural Network (RecNN), a type of models which compose words or phrases recursively over syntactic tree structures, has been proven to have superior ability to obtain sentence representation for a variety of NLP tasks. However,…
The New York Times (NYT) games have found widespread popularity in recent years and reportedly account for an increasing fraction of the newspaper's readership. In this paper, we bring the computational lens to the study of New York Times…
We present an approach to support partiality in type-level computation without compromising expressiveness or type safety. Existing frameworks for type-level computation either require totality or implicitly assume it. For example, type…
Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…
We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and…
Pattern-Based Constraint Satisfaction and Logic Puzzles develops a pure logic, pattern-based perspective of solving the finite Constraint Satisfaction Problem (CSP), with emphasis on finding the "simplest" solution. Different ways of…
(We apologize for pidgin LaTeX) Schlipf \cite{sch91} proved that Stable Logic Programming (SLP) solves all $\mathit{NP}$ decision problems. We extend Schlipf's result to prove that SLP solves all search problems in the class $\mathit{NP}$.…
We develop a class of integrals on a manifold M called exponential iterated integrals, an extension of K. T. Chen's iterated integrals. It is shown that the matrix entries of any upper triangular representation of the fundamental group of M…
The Parks Puzzle is a paper-and-pencil puzzle game that is classically played on a square grid with different colored regions (the parks). The player needs to place a certain number of "trees" in each row, column, and park such that none…
Our objective in this project is three-fold, the first two covered in this paper. In tropical mathematics, as well as other mathematical theories involving semirings, when trying to formulate the tropical versions of classical algebraic…
High-quality mathematical and logical datasets with verifiable answers are essential for strengthening the reasoning capabilities of large language models (LLMs). While recent data augmentation techniques have facilitated the creation of…
In the nineties Immerman and Medina initiated the search for syn- tactic tools to prove NP-completeness. In their work, amongst several results, they conjecture that the NP-completeness of a problem defined by the conjunction of a sentence…
As language models master existing reasoning benchmarks, we need new challenges to evaluate their cognitive frontiers. Puzzle-solving events are rich repositories of challenging multimodal problems that test a wide range of advanced…
Patterned self-assembly tile set synthesis PATS is the problem of finding a minimal tile set which uniquely self-assembles into a given pattern. Czeizler and Popa proved the NP-completeness of PATS and Seki showed that the PATS problem is…
Recent research has applied modal substitution calculus (MSC) and its variants to characterize various computational frameworks such as graph neural networks (GNNs) and distributed computing systems. For example, it has been shown that the…
In healthcare applications, understanding how machine/deep learning models make decisions is crucial. In this study, we introduce a neural network framework, $\textit{Truth Table rules}$ (TT-rules), that combines the global and exact…
The Fewest Clues Problem (FCP) framework has been introduced to study the complexity of determining whether a solution to an \NP~problem can be uniquely identified by specifying a subset of the certificate. For a given problem $P \in \NP$,…