相关论文: A Coalgebraic Approach to Kleene Algebra with Test…
When does a deterministic computational model define a probability distribution? What are its properties? This work formalises and settles this stochasticity problem for weighted automata, and its generalisation cost register automata…
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…
We investigate the applicability of the formalism of quantum mechanics to everyday life. It seems to be directly relevant for situations in which the very act of coming to a conclusion or decision on one issue affects one's confidence about…
We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic)…
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…
We consider the task of automated theorem proving, a key AI task. Deep learning has shown promise for training theorem provers, but there are limited human-written theorems and proofs available for supervised learning. To address this…
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…
Independence-friendly logic is a conservative extension of first-order logic that has the same expressive power as existential second-order logic. In her Ph.D. thesis, Dechesne introduces a variant of independence-friendly logic called IFG…
We present a system for the investigation of computational properties of categorial grammar parsing based on a labelled analytic tableaux theorem prover. This proof method allows us to take a modular approach, in which the basic grammar can…
We show that the axioms of Weak Kleene Algebra (WKA) are sound and complete for the theory of regular expressions modulo simulation equivalence, assuming their completeness for monodic trees (as conjectured by Takai and Furusawa).
This research started with an algebra for reasoning about rely/guarantee concurrency for a shared memory model. The approach taken led to a more abstract algebra of atomic steps, in which atomic steps synchronise (rather than interleave)…
Reactive programs combine traditional sequential programming constructs with primitives to allow communication with other concurrent agents. They are ubiquitous in modern applications, ranging from components systems and web services, to…
First we identify the free algebras of the class of algebras of binary relations equipped with the composition and domain operations. Elements of the free algebras are pointed labelled finite rooted trees. Then we extend to the analogous…
What is Sequence Algebra? This is a question that any teacher or student of mathematics or computer science can engage with. Sequences are in Calculus, Combinatorics, Statistics and Computation. They are foundational, a step up from number…
Given a universal Horn formula of Kleene algebra with hypotheses of the form r = 0, it is already known that we can efficiently construct an equation which is valid if and only if the Horn formula is valid. This is an example of…
We provide a method, based on automata theory, to mechanically prove the correctness of many numeration systems based on Fibonacci numbers. With it, long case-based and induction-based proofs of correctness can be replaced by simply…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
Within the tensor product $K \mathop{\otimes_{\cal R}} C_2'$ of any ${}^*$-continuous Kleene algebra $K$ with the polycyclic ${}^*$-continuous Kleene algebra $C_2'$ over two bracket pairs there is a copy of the fixed-point closure of $K$:…
Induction is typically formalized as a rule or axiom extension of the LK-calculus. While this extension of the sequent calculus is simple and elegant, proof transformation and analysis can be quite difficult. Theories with an induction…