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Reinforcement learning based adaptive/approximate dynamic programming (ADP) is a powerful technique to determine an approximate optimal controller for a dynamical system. These methods bypass the need to analytically solve the nonlinear…
Dropped Pronouns (DP) in which pronouns are frequently dropped in the source language but should be retained in the target language are challenge in machine translation. In response to this problem, we propose a semi-supervised approach to…
Temporal Point Processes (TPP) with partial likelihoods involving a latent structure often entail an intractable marginalization, thus making inference hard. We propose a novel approach to Maximum Likelihood Estimation (MLE) involving…
A coverage type generalizes refinement types found in many functional languages with support for must-style underapproximate reasoning. Property-based testing frameworks are one particularly useful domain where such capabilities are useful…
We show that (local) confluence of terminating locally constrained rewrite systems is undecidable, even when the underlying theory is decidable. Several confluence criteria for logically constrained rewrite systems are known. These were…
Functional dependencies -- traditional, approximate and conditional are of critical importance in relational databases, as they inform us about the relationships between attributes. They are useful in schema normalization, data…
Bisimulation is crucial for verifying process equivalence in probabilistic systems. This paper presents a novel logical framework for analyzing bisimulation in probabilistic parameterized systems, namely, infinite families of finite-state…
Byte-Pair Encoding (BPE) is a widely used method for subword tokenization, with origins in grammar-based text compression. It is employed in a variety of language processing tasks such as machine translation or large language model (LLM)…
In database theory, the term $\textit{database transformation}$ was used to refer to a unifying treatment for computable queries and updates. Recently, it was shown that non-deterministic database transformations can be captured exactly by…
Answer Set Programming (ASP) solvers are highly-tuned and complex procedures that implicitly solve the consistency problem, i.e., deciding whether a logic program admits an answer set. Verifying whether a claimed answer set is formally a…
The maximum type-I and type-II error exponents associated with the newly introduced almost-fixed-length hypothesis testing is characterized. In this class of tests, the decision-maker declares the true hypothesis almost always after…
We try to understand complete types over a somewhat saturated model of a complete first order theory which is dependent (previously called NIP), by "decomposition theorems for such types". Our thesis is that the picture of dependent theory…
Value Iteration is a widely used algorithm for solving Markov Decision Processes (MDPs). While previous studies have extensively analyzed its convergence properties, they primarily focus on convergence with respect to the infinity norm. In…
This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis. The aim of this introduction is to present…
Probabilistic behavior is omnipresent in computer controlled systems, in particular, so-called safety-critical hybrid systems, because of various reasons, like uncertain environments, or fundamental properties of nature. In this paper, we…
We present a formally verified framework for patent analysis as a hybrid AI + Lean 4 pipeline. The DAG-coverage core (Algorithm 1b) is fully machine-verified once bounded match scores are fixed. Freedom-to-operate, claim-construction…
In this paper, I develop a refinement of stability for matching markets with incomplete information. I introduce Information-Credible Pairwise Stability (ICPS), a solution concept in which deviating pairs can use credible, costly tests to…
Dependent pattern matching is a key feature in dependently typed programming. However, there is a theory-practice disconnect: while many proof assistants implement pattern matching as primitive, theoretical presentations give semantics to…
We present a general framework for applying machine-learning algorithms to the verification of Markov decision processes (MDPs). The primary goal of these techniques is to improve performance by avoiding an exhaustive exploration of the…
The framework Pure Type System (PTS) offers a simple and general approach to designing and formalizing type systems. However, in the presence of dependent types, there often exist certain acute problems that make it difficult for PTS to…