Related papers: Scalar and Vectorial mu-calculus with Atoms
Let R be a commutative ring with unity, M be an unitary R-module and {\Gamma} be a simple graph. This research article is an interplay of combinatorial and algebraic properties of M . We show a combinatorial object completely determines an…
Evaluation of basic integrals over Gaussian functions, traditionally utilized for electronic structure computations on molecules and solids, is discussed in a pedagogical form.
We study a quantum version of the sequential game illustrating problems connected with making rational decisions. We compare the results that the two models (quantum and classical) yield. In the quantum model intransitivity gains importance…
The mu-calculus is a powerful tool for specifying and verifying transition systems, including those with both demonic and angelic choice; its quantitative generalisation qMu extends that to probabilistic choice. We show that for a…
The polyadic mu-calculus is a modal fixpoint logic whose formulas define relations of nodes rather than just sets in labelled transition systems. It can express exactly the polynomial-time computable and bisimulation-invariant queries on…
We study semantic and syntactic properties of spherical orders and their elementary theories, including finite and dense orders and their theories. It is shown that theories of dense $n$-spherical orders are countably categorical and…
In this paper we give an alternative construction using Monk like algebras that are binary generated to show that the class of strongly representable atom structures is not elementary. The atom structures of such algebras are cylindric…
Due to the undecidability of most type-related properties of System F like type inhabitation or type checking, restricted polymorphic systems have been widely investigated (the most well-known being ML-polymorphism). In this paper we…
This paper deals with topos-theoretic truth-value valuations of quantum propositions. Concretely, a mathematical framework of a specific type of modal approach is extended to the topos theory, and further, structures of the obtained…
The topological $\mu$-calculus has gathered attention in recent years as a powerful framework for representation of spatial knowledge. In particular, spatial relations can be represented over finite structures in the guise of weakly…
The coalgebraic approach to modal logic provides a uniform framework that captures the semantics of a large class of structurally different modal logics, including e.g. graded and probabilistic modal logics and coalition logic. In this…
We introduce a new game-theoretic semantics (GTS) for the modal mu-calculus. Our so-called bounded GTS replaces parity games with alternative evaluation games where only finite paths arise; infinite paths are not needed even when the…
Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We give a general discussion of such models and their rationality criteria. We study exchangeability assessments…
We discuss and compare complexity measures for the modal $\mu$-calculus, focusing on size and alternation depth. As a yardstick we take Wilke's alternating tree automata, which we shall call parity formulas in the text. Building on work by…
Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of "predict and verify" cannot be applied to testing quantum mechanics in this limit of high complexity.…
The molecular computing has been successfully employed to solve more and more complex computation problems. However, as an important complex problem, the model checking are still far from fully resolved under the circumstance of molecular…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
Automata operating on infinite objects feature prominently in the theory of the modal $\mu$-calculus. One such application concerns the tableau games introduced by Niwi\'{n}ski & Walukiewicz, of which the winning condition for infinite…
This tutorial introduces quantum computing with a focus on the applicability of formal methods in this relatively new domain. We describe quantum circuits and convey an understanding of their inherent combinatorial nature and the…
We introduce a new game-theoretic semantics (GTS) for the modal mu-calculus. Our so-called bounded GTS replaces parity games with alternative evaluation games where only finite paths arise; infinite paths are not needed even when the…