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We prove rich algebraic structures of the solution space for 2-layer neural networks with quadratic activation and $L_2$ loss, trained on reasoning tasks in Abelian group (e.g., modular addition). Such a rich structure enables…

Planning methods struggle with computational intractability in solving task-level problems in large-scale environments. This work explores leveraging the commonsense knowledge encoded in LLMs to empower planning techniques to deal with…

While Large Language Models (LLMs) have recently shown promise in Automated Heuristic Design (AHD), existing approaches typically formulate AHD around constructive priority rules or parameterized local search guidance, thereby restricting…

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,…

Semantic operators have increasingly become integrated within data systems to enable processing data using Large Language Models (LLMs). Despite significant recent effort in improving these operators, their accuracy is limited due to a…

Humans continuously make new discoveries, and understanding temporal sequence of events leading to these breakthroughs is essential for advancing science and society. This ability to reason over time allows us to identify future steps and…

Real world applications as in industry and robotics need modelling rich and diverse automated planning problems. Their resolution usually requires coordinated and concurrent action execution. In several cases, these problems are naturally…

We develop a simple functional programming language aimed at manipulating infinite, but first-order definable structures, such as the countably infinite clique graph or the set of all intervals with rational endpoints. Internally, such sets…

We present team semantics for two of the most important linear and branching time specification languages, Linear Temporal Logic (LTL) and Computation Tree Logic (CTL). With team semantics, LTL is able to express hyperproperties, which have…

Finding a denotational semantics for higher order quantum computation is a long-standing problem in the semantics of quantum programming languages. Most past approaches to this problem fell short in one way or another, either limiting the…

Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited…

Pre-trained large language models (LLMs) have been demonstrated to possess intrinsic reasoning capabilities that can emerge naturally when expanding the response space. However, the neural representation mechanisms underlying these…

Pull-tabbing is an evaluation technique for functional logic programs which computes all non-deterministic results in a single graph structure. Pull-tab steps are local graph transformations to move non-deterministic choices towards the…

Global sentence information is crucial for sequence labeling tasks, where each word in a sentence must be assigned a label. While BiLSTM models are widely used, they often fail to capture sufficient global context for inner words. Previous…

Parallel test-time scaling (TTS) is a pivotal approach for enhancing large language models (LLMs), typically by sampling multiple token-based chains-of-thought in parallel and aggregating outcomes through voting or search. Recent advances…

Real-world document question answering is challenging. Analysts must synthesize evidence across multiple documents and different parts of each document. However, any fixed LLM context window can be exceeded as document collections grow. A…

Speech separation (SS) has advanced significantly with neural network-based methods, showing improved performance on signal-level metrics. However, these methods often struggle to maintain speech intelligibility in the separated signals,…

We study temporally extended goals expressed in Pure-Past LTL (PPLTL). PPLTL is particularly interesting for expressing goals since it allows to express sophisticated tasks as in the Formal Methods literature, while the worst-case…

Syntactic NL or succinctly SNL was first introduced in 2017, analogously to SNP, as a ``syntactically''-defined natural subclass of NL (nondeterministic logarithmic-space complexity class) using a restricted form of logical sentences,…

Description Logics (DLs) are used in knowledge-based systems to represent and reason about terminological knowledge of the application domain in a semantically well-defined manner. In this thesis, we establish a number of novel complexity…