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Basic results in combinatorial mathematics provide the foundation for a theory and calculus for reasoning about sequential behavior. A key concept of the theory is a generalization of Boolean implicant which deals with statements of the…
Proper scoring rules evaluate the quality of probabilistic predictions, playing an essential role in the pursuit of accurate and well-calibrated models. Every proper score decomposes into two fundamental components -- proper calibration…
Algorithms often have tunable parameters that impact performance metrics such as runtime and solution quality. For many algorithms used in practice, no parameter settings admit meaningful worst-case bounds, so the parameters are made…
Refinement calculus provides a structured framework for the progressive and modular development of programs, ensuring their correctness throughout the refinement process. This paper introduces a refinement calculus tailored for quantum…
We consider the broad problem of analyzing safety properties of asynchronous concurrent programs under arbitrary thread interleavings. Delay-bounded deterministic scheduling, introduced in prior work, is an efficient bug-finding technique…
This paper studies a difference operator for stochastic systems whose specifications are represented by Abstract Probabilistic Automata (APAs). In the case refinement fails between two specifications, the target of this operator is to…
In this work we establish and investigate connections between causality for query answers in databases, database repairs wrt. denial constraints, and consistency-based diagnosis. The first two are relatively new problems in databases, and…
Decision paralysis, i.e. hesitation, freezing, or failure to act despite full knowledge and motivation, poses a challenge for choice models that assume options are already specified and readily comparable. Drawing on qualitative reports in…
When using graphs and graph transformations to model systems, consistency is an important concern. While consistency has primarily been viewed as a binary property, i.e., a graph is consistent or inconsistent with respect to a set of…
This paper studies the Byzantine Agreement problem where the nodes have access to a predictor that flags nodes for suspicion of faulty (Byzantine) behavior. We focus on algorithmic resilience -- the maximum number of faulty nodes an…
The inner alignment problem, which asserts whether an arbitrary artificial intelligence (AI) model satisfices a non-trivial alignment function of its outputs given its inputs, is undecidable. This is rigorously proved by Rice's theorem,…
The dominant industry response to AI-generated code quality problems is to deploy AI reviewers. This paper argues that this response is structurally circular when executable specifications are absent: without an external reference, both the…
Retrieval-augmented generation (RAG) improves large language models (LLMs) by incorporating external evidence, but it also introduces knowledge conflicts when retrieved contextual knowledge (CK) and parametric knowledge (PK) disagree or are…
A/B testing refers to the task of determining the best option among two alternatives that yield random outcomes. We provide distribution-dependent lower bounds for the performance of A/B testing that improve over the results currently…
The correctness of most randomized distributed algorithms is expressed by a statement of the form ``some predicate of the executions holds with high probability, regardless of the order in which actions are scheduled''. In this paper, we…
We give a sequential model for noninterference security including probability (but not demonic choice), thus supporting reasoning about the likelihood that high-security values might be revealed by observations of low-security activity. Our…
Robotic systems often use predictive uncertainty to decide whether to act autonomously or defer to a fallback policy. In threshold-gated autonomy, uncertainty matters mainly through its ability to rank likely errors. Standard metrics such…
Large reasoning models (LRMs) already possess a latent capacity for long chain-of-thought reasoning. Prior work has shown that outcome-based reinforcement learning (RL) can incidentally elicit advanced reasoning behaviors such as…
Precedential constraint is one foundation of case-based reasoning in AI and Law. It generally assumes that the underlying set of precedents must be consistent. To relax this assumption, a generalized notion of the reason model has been…
The trustworthiness of AI decision-making systems is increasingly important. A key feature of such systems is the ability to provide recommendations for how an individual may reverse a negative decision, a problem known as algorithmic…