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Education in the practical applications of logic and proving such as the formal specification and verification of computer programs is substantially hampered by the fact that most time and effort that is invested in proving is actually…
The standard approach to analyzing the asymptotic complexity of probabilistic programs is based on studying the asymptotic growth of certain expected values (such as the expected termination time) for increasing input size. We argue that…
We consider the predictive problem of supervised ranking, where the task is to rank sets of candidate items returned in response to queries. Although there exist statistical procedures that come with guarantees of consistency in this…
Usually, probabilistic automata and probabilistic grammars have crisp symbols as inputs, which can be viewed as the formal models of computing with values. In this paper, we first introduce probabilistic automata and probabilistic grammars…
Finding whether a linear-constraint loop has a linear ranking function is an important key to understanding the loop behavior, proving its termination and establishing iteration bounds. If no preconditions are provided, the decision problem…
Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…
Learning to rank is a supervised learning problem where the output space is the space of rankings but the supervision space is the space of relevance scores. We make theoretical contributions to the learning to rank problem both in the…
We propose and investigate probabilistic guarantees for the adversarial robustness of classification algorithms. While traditional formal verification approaches for robustness are intractable and sampling-based approaches do not provide…
Recently, there has been an increasing interest in the bottom-up evaluation of the semantics of logic programs with complex terms. The presence of function symbols in the program may render the ground instantiation infinite, and finiteness…
Logically constrained term rewriting is a relatively new rewriting formalism that naturally supports built-in data structures, such as integers and bit vectors. In the analysis of logically constrained term rewrite systems (LCTRSs),…
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…
We provide a constraint based computational model of linear precedence as employed in the HPSG grammar formalism. An extended feature logic which adds a wide range of constraints involving precedence is described. A sound, complete and…
We study the differential properties of higher-order statistical probabilistic programs with recursion and conditioning. Our starting point is an open problem posed by Hongseok Yang: what class of statistical probabilistic programs have…
We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an…
We extend our techniques developed in our earlier paper appeared in Computational Complexity, 2017 (preprint: arXiv:1508.00690) to obtain a deterministic polynomial time algorithm for computing the non-commutative rank together with…
Large language models (LLMs) offer substantial promise for text classification in political science, yet their effectiveness often depends on high-quality prompts and exemplars. To address this, we introduce a three-stage framework that…
Tiny Recursive Models (TRM) solve complex reasoning tasks with a fraction of the parameters of modern large language models (LLMs) by iteratively refining a latent state and final answer. While powerful, their deterministic recursion can…
Termination of programs, i.e., the absence of infinite computations, ensures the existence of normal forms for all initial expressions, thus providing an essential ingredient for the definition of a normalization semantics for functional…
There are many techniques and tools to prove termination of C programs, but up to now these tools were not very powerful for fully automated termination proofs of programs whose termination depends on recursive data structures like lists.…
Final coalgebras as "categorical greatest fixed points" play a central role in the theory of coalgebras. Somewhat analogously, most proof methods studied therein have focused on greatest fixed-point properties like safety and bisimilarity.…