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We describe here a simple application of rational trees to the implementation of an interpreter for a procedural language written in a logic programming language. This is possible in languages designed to support rational trees (such as…
While chain-of-thought prompting with Best-of-N (BoN) selection has become popular for mathematical reasoning in large language models (LLMs), its linear structure fails to capture the branching and exploratory nature of complex…
Automated agent workflows can enhance the problem-solving ability of large language models (LLMs), but common search strategies rely on stochastic exploration and often traverse implausible branches. This occurs because current pipelines…
We describe mts, a generic framework for parallelizing certain types of tree search programs including reverse search, backtracking, branch and bound and satisfiability testing. It abstracts and generalizes the ideas used in parallelizing…
Search engines play a vital role in day to day life on internet. People use search engines to find content on internet. Cloud computing is the computing concept in which data is stored and accessed with the help of a third party server…
Optimization modeling is one of the most crucial but technical parts of operations research (OR). To automate the modeling process, existing works have leveraged large language models (LLMs), prompting them to break down tasks into steps…
A tremendous range of design tasks in materials, physics, and biology can be formulated as finding the optimum of an objective function depending on many parameters without knowing its closed-form expression or the derivative. Traditional…
We investigate optimizing quantum tree search algorithms by employing a nested Grover Algorithm. This approach seeks to enhance results compared to previous Grover-based methods by expanding the tree of partial assignments to a specific…
Large language models (LLMs) have demonstrated impressive capability in reasoning and planning when integrated with tree-search-based prompting methods. However, since these methods ignore the previous search experiences, they often make…
Recent advances in reinforcement learning (RL) have significantly enhanced the agentic capabilities of large language models (LLMs). In long-term and multi-turn agent tasks, existing approaches driven solely by outcome rewards often suffer…
Long-horizon planning in realistic environments requires the ability to reason over sequential tasks in high-dimensional state spaces with complex dynamics. Classical motion planning algorithms, such as rapidly-exploring random trees, are…
Wavelet trees are widely used in the representation of sequences, permutations, text collections, binary relations, discrete points, and other succinct data structures. We show, however, that this still falls short of exploiting all of the…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on frameworks for reasoning about path expressions…
Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs). Within this framework, a CSP instance is decomposed into a number of sub-problems, called views,…
In the context of tree-search stochastic planning algorithms where a generative model is available, we consider on-line planning algorithms building trees in order to recommend an action. We investigate the question of avoiding re-planning…
Recent advancements in large language models have significantly improved their context windows, yet challenges in effective long-term memory management remain. We introduce MemTree, an algorithm that leverages a dynamic, tree-structured…
We present a functional programming language for specifying constraints over tree-shaped data. The language allows for Haskell-like algebraic data types and pattern matching. Our constraint compiler CO4 translates these programs into…
Symbolic indefinite integration in Computer Algebra Systems such as Maple involves selecting the most effective algorithm from multiple available methods. Not all methods will succeed for a given problem, and when several do, the results,…
In low-dimensional topology, many important decision algorithms are based on normal surface enumeration, which is a form of vertex enumeration over a high-dimensional and highly degenerate polytope. Because this enumeration is subject to…
``Algorithms with predictions'', or ``learning-augmented algorithms'', has proved to be an extremely useful paradigm for combining machine learning with traditional algorithms. One of the textbook settings for this is searching a sorted…