Related papers: Algebraic Notions of Termination
We consider the functions in two variables on an arbitrary poset, for which the convolution operation is defined. We obtain the generalization of incidence algebra and describe its properties: invertibility, the Jackobson radical,…
We first establish several general properties of modality of algebraic group actions. In particular, we introduce the notion of a modality-regular action and prove that every visible action is modality-regular. Then, using these results, we…
An alternative mathematics based on qualitative plurality of finiteness is developed to make non-standard mathematics independent of infinite set theory. The vague concept "accessibility" is used coherently within finite set theory whose…
We see how nested sequents, a natural generalisation of hypersequents, allow us to develop a systematic proof theory for modal logics. As opposed to other prominent formalisms, such as the display calculus and labelled sequents, nested…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
We study modular forms of some congruence subgroups. In this paper, we treat the cases level is 2-power, 3-power or 5. Structures of graded rings and many identities of infinite sum or infinite product are given. Theory of rational (1/3,…
Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often…
In this paper, we develop an explicit method to express finite algebraic numbers (in particular, certain idempotents among them) in terms of linear recurrent sequences, and give applications to the characterization of the splitting primes…
The modelling, specification and study of the semantics of concurrent reactive systems have been interesting research topics for many years now. The aim of this thesis is to exploit the strengths of the (co)algebraic framework in modelling…
Propositional logic serves as a fundamental cornerstone in mathematical logic. This paper delves into a semiring characterization of propositional logic, employing the Gr\"oebner-Shirshov basis theory to furnish an algebraic framework for…
We carry out a proof theoretic analysis of the wellfoundedness of recursive path orders in an abstract setting. We outline a very general termination principle and extract from its wellfoundedness proof subrecursive bounds on the size of…
Alternating parity automata (APAs) provide a robust formalism for modelling infinite behaviours and play a central role in formal verification. Despite their widespread use, the algebraic theory underlying APAs has remained largely…
The commutative and homological algebra of modules over posets is developed, as closely parallel as possible to the algebra of finitely generated modules over noetherian commutative rings, in the direction of finite presentations, primary…
This is a survey on the finite basis problem for varieties of algebraic systems. Our exposition is in two directions: (i) We give numerous examples of varieties which are not finitely based. (ii) We give examples of important varieties with…
The paper is devoted to modal properties of the ternary strict betweenness relation as used in the development of various systems of geometry. We show that such a relation is non-definable in a basic similarity type with a binary operator…
Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We exhibit such a finite semantics for a polymorphic purely linear…
In this article, we present the basic definitions of modules and Lie semialgebras over semirings with a negation map. Our main example of a semiring with a negation map is ELT algebras, and some of the results in this article are formulated…
Semiring semantics for first-order logic provides a way to trace how facts represented by a model are used to deduce satisfaction of a formula. Team semantics is a framework for studying logics of dependence and independence in diverse…
G\"odel's second incompleteness theorem is standardly understood as showing that no sufficiently strong, consistent theory of arithmetic can prove its own consistency, a result typically interpreted against a model-theoretic background in…
We introduce the notion of ends for algebras. The definition is analogous to the one in geometric group theory. We establish some relations to growth conditions and cyclic cohomology.