Dexter Kozen
We give a decision procedure and proof of correctness for the equational theory of probabilistic Kleene algebra with angelic nondeterminism introduced in Ong, Ma, and Kozen (2025).
We develop StacKAT, a network verification language featuring loops, finite state variables, nondeterminism, and - most importantly - access to a stack with accompanying push and pop operations. By viewing the variables and stack as the…
We introduce a version of probabilistic Kleene algebra with angelic nondeterminism and a corresponding class of automata. Our approach implements semantics via distributions over multisets in order to overcome theoretical barriers arising…
Various categories have been proposed as targets for the denotational semantics of higher-order probabilistic programming languages. One such proposal involves joint probability distributions (couplings) used in Bayesian statistical models…
Programs increasingly rely on randomization in applications such as cryptography and machine learning. Analyzing randomized programs has been a fruitful research direction, but there is a gap when programs also exploit nondeterminism (for…
Guarded Kleene Algebra with Tests (GKAT for short) is an efficient fragment of Kleene Algebra with Tests, suitable for reasoning about simple imperative while-programs. Following earlier work by Das and Pous on Kleene Algebra, we study GKAT…
We give a lightweight alternative construction of Jacobs's distributive law for multisets and distributions that does not involve any combinatorics. We first give a distributive law for lists and distributions, then apply a general theorem…
Early programming models for software-defined networking (SDN) focused on basic features for controlling network-wide forwarding paths, but more recent work has considered richer features, such as packet scheduling and queueing, that affect…
Eklund et al. (2002) present a graphical technique aimed at simplifying the verification of various category-theoretic constructions, notably the composition of monads. In this note we take a different approach involving string rewriting.…
We study varieties of certain ordered $\Sigma$-algebras with restricted completeness and continuity properties. We give a general characterization of their free algebras in terms of submonads of the monad of $\Sigma$-coterms. Varieties of…
We introduce Probabilistic Guarded Kleene Algebra with Tests (ProbGKAT), an extension of GKAT that allows reasoning about uninterpreted imperative programs with probabilistic branching. We give its operational semantics in terms of special…
We introduce Concurrent NetKAT (CNetKAT), an extension of NetKAT with operators for specifying and reasoning about concurrency in scenarios where multiple packets interact through state. We provide a model of the language based on…
Guarded Kleene Algebra with Tests (GKAT) is an efficient fragment of KAT, as it allows for almost linear decidability of equivalence. In this paper, we study the (co)algebraic properties of GKAT. Our initial focus is on the fragment that…
Guarded Kleene Algebra with Tests (GKAT) is a variation on Kleene Algebra with Tests (KAT) that arises by restricting the union ($+$) and iteration ($*$) operations from KAT to predicate-guarded versions. We develop the (co)algebraic theory…
Algorithms for deriving Huffman codes and the recently developed algorithm for compiling PIFO trees to trees of fixed shape (Mohan et al. 2022) are similar, but work with different underlying algebraic operations. In this paper, we exploit…
We propose a coalgebraic model for constructing and reasoning about state-based protocols that implement efficient reductions among random processes. We provide basic tools that allow efficient protocols to be constructed in a compositional…
We define sound and adequate denotational and operational semantics for the stochastic lambda calculus. These two semantic approaches build on previous work that used similar techniques to reason about higher-order probabilistic programs,…
Automata models for data languages (i.e. languages over infinite alphabets) often feature either global or local freshness operators. We show that Bollig et al.'s session automata, which focus on global freshness, are equivalent to regular…
Stone-type dualities provide a powerful mathematical framework for studying properties of logical systems. They have recently been fruitfully explored in understanding minimisation of various types of automata. In Bezhanishvili et al.…
This paper presents McNetKAT, a scalable tool for verifying probabilistic network programs. McNetKAT is based on a new semantics for the guarded and history-free fragment of Probabilistic NetKAT in terms of finite-state, absorbing Markov…