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Large language models (LLMs) show strong performance across natural language processing (NLP), mathematical reasoning, and programming, and recent large reasoning models (LRMs) further emphasize explicit reasoning. Yet their computational…
We propose a decision-theoretic framework for computational complexity, complementary to classical theory: moving from syntactic exactness (Turing / Shannon) to semantic simulability (Le Cam). While classical theory classifies problems by…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
While pre-trained language models (LMs) have brought great improvements in many NLP tasks, there is increasing attention to explore capabilities of LMs and interpret their predictions. However, existing works usually focus only on a certain…
In this paper we investigate the theoretical foundation of a new bottom-up semantics for linear logic programs, and more precisely for the fragment of LinLog that consists of the language LO enriched with the constant 1. We use constraints…
LLMs have made significant progress in the field of mathematical reasoning, but whether they have true the mathematical understanding ability is still controversial. To explore this issue, we propose a new perturbation framework to evaluate…
In the previous article, we presented a quantum-inspired framework for modeling semantic representation and processing in Large Language Models (LLMs), drawing upon mathematical tools and conceptual analogies from quantum mechanics to offer…
Current evaluation paradigms for large language models (LLMs) represent a critical blind spot in AI research--relying on opaque numerical metrics that conceal fundamental limitations in spatial reasoning while providing no intuitive…
Recent progress in Multi-modal Large Language Models (MLLMs) has enabled step-by-step multi-modal mathematical reasoning by performing visual operations based on the textual instructions. A promising approach uses code as an intermediate…
Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…
While large language models (LLMs) have shown strong performance in math and logic reasoning, their ability to handle combinatorial optimization (CO) -- searching high-dimensional solution spaces under hard constraints -- remains…
In experimental applications of bounded-reasoning models, behavior is often summarized by distributions of "levels". We argue that such summaries conflate two conceptually distinct dimensions: a player's type, capturing beliefs about what…
Though many safety-critical software systems use floating point to represent real-world input and output, programmers usually have idealized versions in mind that compute with real numbers. Significant deviations from the ideal can cause…
Large language models (LLMs) have recently shown strong reasoning capabilities beyond traditional language tasks, motivating their use for numerical optimization. This paper presents LLMize, an open-source Python framework that enables…
Large Language Models (LLMs) have demonstrated remarkable ability in long-horizon Task and Motion Planning (TAMP) by translating clear and straightforward natural language problems into formal specifications such as the Planning Domain…
Purpose: This study extends the structural theory of finite commutative ternary $\Gamma$-semirings into a computational and categorical framework for explicit classification and constructive reasoning. Methods: Constraint-driven enumeration…
Modern answer set programming solvers such as CLINGO support advanced language constructs that improve the expressivity and conciseness of logic programs. Conditional literals are one such construct. They form "subformulas" that behave as…
In this thesis, we introduce a new quantum Turing machine (QTM) model that supports general quantum operators, together with its pushdown, counter, and finite automaton variants, and examine the computational power of classical and quantum…
Large language models (LLMs) process and predict sequences containing text to answer questions, and address tasks including document summarization, providing recommendations, writing software and solving quantitative problems. We provide a…
Large Language Models (LLMs) have been widely used to automate programming tasks. Their capabilities have been evaluated by assessing the quality of generated code through tests or proofs. The extent to which they can reason about code is a…