Related papers: Brzozowski Goes Concurrent - A Kleene Theorem for …
Pomset automata are an operational model of weak bi-Kleene algebra, which describes programs that can fork an execution into parallel threads, upon completion of which execution can join to resume as a single thread. We characterize a…
Kleene algebra with tests (KAT) was introduced as an algebraic structure to model and reason about classic imperative programs, i.e. sequences of discrete transitions guarded by Boolean tests. This paper introduces two generalisations of…
This work studies the question of learning probabilistic deterministic automata from language models. For this purpose, it focuses on analyzing the relations defined on algebraic structures over strings by equivalences and similarities on…
Pretrained language models (PLM) achieve surprising performance on the Choice of Plausible Alternatives (COPA) task. However, whether PLMs have truly acquired the ability of causal reasoning remains a question. In this paper, we investigate…
In this paper, we present a systematic way of deriving (1) languages of (generalised) regular expressions, and (2) sound and complete axiomatizations thereof, for a wide variety of systems. This generalizes both the results of Kleene (on…
Data words with binders formalize concurrently allocated memory. Most name-binding mechanisms in formal languages, such as the $\lambda$-calculus, adhere to properly nested scoping. In contrast, stateful programming languages with explicit…
We introduce the Concurrent Modular Agent (CMA), a framework that orchestrates multiple Large-Language-Model (LLM)-based modules that operate fully asynchronously yet maintain a coherent and fault-tolerant behavioral loop. This framework…
We extend the formalisation of confluence results in Kleene algebras to a formalisation of coherent confluence proofs. For this, we introduce the structure of higher globular Kleene algebra, a higher-dimensional generalisation of modal and…
A classical theorem states that the set of languages given by a pushdown automaton coincides with the set of languages given by a context-free grammar. In previous work, we proved the pendant of this theorem in a setting with interaction:…
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…
Automata learning is a popular technique for inferring minimal automata through membership and equivalence queries. In this paper, we generalise learning to the theory of coalgebras. The approach relies on the use of logical formulas as…
We investigate the algebraic reasoning of quantum programs inspired by the success of classical program analysis based on Kleene algebra. One prominent example of such is the famous Kleene Algebra with Tests (KAT), which has furnished both…
Relational verification encompasses information flow security, regression verification, translation validation for compilers, and more. Effective alignment of the programs and computations to be related facilitates use of simpler relational…
We provided (PNSE'2014) expressions for free choice nets having "distributed choice property" which makes the nets "direct product" representable. In a recent work (PNSE'2016), we gave equivalent syntax for a larger class of free choice…
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 the quantum subset construction of orthomodular lattice-valued finite automata, then we show the equivalence between orthomodular lattice-valued finite automata, orthomodular lattice-valued deterministic finite automata and…
Kleene algebra with tests (KAT) is a foundational equational framework for reasoning about programs, which has found applications in program transformations, networking and compiler optimizations, among many other areas. In his seminal…
Higher-dimensional automata (HDA) are a model of concurrency that models simultaneous execution of events using higher dimensional cells. HDA recognize languages of pomsets, a generalization of finite words whose letters are partially…
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…
Pomsets are a promising formalism for concurrent programs based on partially ordered sets. Among this class, series-parallel pomsets admit a convenient linear representation and can be recognized by simple algebraic structures known as…