Related papers: Structure and Problem Hardness: Goal Asymmetry and…
Foundational optimization embeddings have recently emerged as powerful pre-trained representations for mixed-integer programming (MIP) problems. These embeddings were shown to enable cross-domain transfer and reduce reliance on…
In the first paper (part I) of this series of two, we introduce four novel definitions of the ODT problems: three for size-constrained trees and one for depth-constrained trees. These definitions are stated unambiguously through executable…
Efficient implementations of DPLL with the addition of clause learning are the fastest complete Boolean satisfiability solvers and can handle many significant real-world problems, such as verification, planning and design. Despite its…
Constraint Satisfaction Problem (CSP) is a fundamental algorithmic problem that appears in many areas of Computer Science. It can be equivalently stated as computing a homomorphism $\mbox{$\bR \rightarrow \bGamma$}$ between two relational…
Constrained-random simulation is the predominant approach used in the industry for functional verification of complex digital designs. The effectiveness of this approach depends on two key factors: the quality of constraints used to…
AI-Scientist systems that use large language models to automate research risk generating spurious discoveries through uncontrolled multiple testing. We present a functional architecture that enforces statistical rigor at two levels: a…
In a field of research about general reasoning mechanisms, it is essential to have appropriate benchmarks. Ideally, the benchmarks should reflect possible applications of the developed technology. In AI Planning, researchers more and more…
Path planning is an active area of research essential for many applications in robotics. Popular techniques include graph-based searches and sampling-based planners. These approaches are powerful but have limitations. This paper continues…
While large language models (LLMs) have recently demonstrated strong potential in solving planning problems, there is a trade-off between flexibility and complexity. LLMs, as zero-shot planners themselves, are still not capable of directly…
Answer Set Programming (ASP) is a well-established declarative paradigm. One of the successes of ASP is the availability of efficient systems. State-of-the-art systems are based on the ground+solve approach. In some applications this…
Answer Set Programming (ASP) is an increasingly popular framework for declarative programming that admits the description of problems by means of rules and constraints that form a disjunctive logic program. In particular, many AI problems…
We introduce and benchmark a stochastic local search heuristic for the NP-complete satisfiability problem 3-SAT that drastically outperforms existing solvers in the notoriously difficult realm of critically hard instances. Our construction…
The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…
We introduce MathConstraint, a hard, adaptive benchmark for evaluating the combinatorial reasoning capabilities of LLMs. We combine constraint satisfaction problems with rigorous solver-based verification and design an adaptive generator to…
The conventional LUT is redundant since practical functions in real-world benchmarks only occupy a small proportion of all the functions. For example, there are only 3881 out of more than $10^{14}$ NPN classes of 6-input functions occurring…
Recent trends in planning research have led to empirical comparison becoming commonplace. The field has started to settle into a methodology for such comparisons, which for obvious practical reasons requires running a subset of planners on…
Neural architecture search is a promising area of research dedicated to automating the design of neural network models. This field is rapidly growing, with a surge of methodologies ranging from Bayesian optimization,neuroevoltion, to…
The constraint satisfaction problem asks to decide if a set of constraints over a relational structure $\mathcal{A}$ is satisfiable (CSP$(\mathcal{A})$). We consider CSP$(\mathcal{A} \cup \mathcal{B})$ where $\mathcal{A}$ is a structure and…
Formal mathematical reasoning remains a critical challenge for artificial intelligence, hindered by limitations of existing benchmarks in scope and scale. To address this, we present FormalMATH, a large-scale Lean4 benchmark comprising…
In this paper we propose the approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. For the same SAT instance…