9 citations · 18 across the 11 of their papers we have counts for
14 papers
GKAT with Hoare Hypotheses
Jurriaan Rot, Todd Schmid, Jana Wagemaker
Guarded Kleene Algebra with Tests (GKAT) is a variant of Kleene algebra which allows for reasoning about simple imperative programs, and which features a decision procedure for pro…
The Algebra of Iterative Constructions
Kevin Batz, Benjamin Lucien Kaminski, Lucas Kehrer +3
Fixed points are a recurring theme in computer science and are often constructed as limits of suitably seeded fixed point iterations. We present the algebra of iterative constructi…
Coalgebraic Path Constraints
Todd Schmid
Axiomatizing covarieties of coalgebras for an endofunctor is less intuitive than axiomatizing varieties of algebras via equations (Dahlqvist and Schmid, 2022). Existing techniques…
A General Completeness Theorem for Skip-free Star Algebras
Tobias Kappé, Todd Schmid
We consider process algebras with branching parametrized by an equational theory T, and show that it is possible to axiomatize bisimilarity under certain conditions on T. Our proof…
Fractals from Regular Behaviours
Todd Schmid, Victoria Noquez, Lawrence S. Moss
We forge connections between the theory of fractal sets obtained as attractors of iterated function systems and process calculi. To this end, we reinterpret Milner's expressions fo…
Probabilistic Guarded KAT Modulo Bisimilarity: Completeness and Complexity
Wojciech Różowski, Tobias Kappé, Dexter Kozen +2
We introduce Probabilistic Guarded Kleene Algebra with Tests (ProbGKAT), an extension of GKAT that allows reasoning about uninterpreted imperative programs with probabilistic branc…
A Complete Inference System for Skip-free Guarded Kleene Algebra with Tests
Tobias Kappé, Todd Schmid, Alexandra Silva
Guarded Kleene Algebra with Tests (GKAT) is a fragment of Kleene Algebra with Tests (KAT) that was recently introduced to reason efficiently about imperative programs. In contrast…
A (Co)Algebraic Framework for Ordered Processes
Todd Schmid
A recently published paper (Schmid, Rozowski, Silva, and Rot, 2022) offers a (co)algebraic framework for studying processes with algebraic branching structures and recursion operat…
Presenting with Quantitative Inequational Theories
Todd Schmid
It came to the attention of myself and the coauthors of (S., Rozowski, Silva, Rot, 2022) that a number of process calculi can be obtained by algebraically presenting the branching…
Processes Parametrised by an Algebraic Theory
Todd Schmid, Wojciech Rozowski, Alexandra Silva +1
We develop a (co)algebraic framework to study a family of process calculi with monadic branching structures and recursion operators. Our framework features a uniform semantics of p…
How to write a coequation
Fredrik Dahlqvist, Todd Schmid
There is a large amount of literature on the topic of covarieties, coequations and coequational specifications, dating back to the early seventies. Nevertheless, coequations have n…
On Star Expressions and Coalgebraic Completeness Theorems
Todd Schmid, Jurriaan Rot, Alexandra Silva
An open problem posed by Milner asks for a proof that a certain axiomatisation, which Milner showed is sound with respect to bisimilarity for regular expressions, is also complete.…
Guarded Kleene Algebra with Tests: Coequations, Coinduction, and Completeness
Todd Schmid, Tobias Kappé, Dexter Kozen +1
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 prop…
Concrete Barriers to Quantifier Elimination in Finite-Dimensional C*-algebras
Christopher J. Eagle, Todd Schmid
Work of Eagle, Farah, Goldbring, Kirchberg, and Vignati shows that the only separable C*-algebras that admit quantifier elimination in continuous logic are $\mathbb{C…