Related papers: Unique Solutions of Guarded Recursive Equations
The chase procedure is a fundamental algorithmic tool in database theory with a variety of applications. A key problem concerning the chase procedure is all-instances termination: for a given set of tuple-generating dependencies (TGDs), is…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
We consider a version of a famous open problem formulated by Kadison, asking whether bounded representations of operator algebras are automatically completely bounded. We investigate this question in the context of amenable operator…
We consider the precedence-constrained scheduling problem to minimize the total weighted completion time. For a single machine several $2$-approximation algorithms are known, which are based on linear programming and network flows. We show…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
We design games for truly concurrent bisimilarities, including strongly truly concurrent bisimilarities and branching truly concurrent bisimilarities, such as pomset bisimilarities, step bisimilarities, history-preserving bisimilarities and…
We prove that solutions to elliptic equations in two variables in divergence form, possibly non-selfadjoint and with lower order terms, satisfy the strong unique continuation property.
Complete residue systems play an integral role in abstract algebra and number theory, and a description is typically found in any number theory textbook. This note provides a concise overview of complete residue systems, including a robust…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
We prove an existence and uniqueness theorem for exact WKB solutions of general singularly perturbed linear second-order ODEs in the complex domain. These include the one-dimensional time-independent complex Schr\"odinger equation. Notably,…
We present a novel construction of recursion operators for scalar second-order integrable multidimensional PDEs with isospectral Lax pairs written in terms of first-order scalar differential operators. Our approach is quite straightforward…
The framework of graded semantics uses graded monads to capture behavioural equivalences of varying granularity, for example as found on the linear-time/branching-time spectrum, over general system types. We describe a generic…
It is widely known that the recursion operator is a very important component of integrability. It allows one to describe in a compact form both hierarchies of the generalized symmetries and infinite series of the local conservation laws. In…
The spi-calculus is a formal model for the design and analysis of cryptographic protocols: many security properties, such as authentication and strong confidentiality, can be reduced to the verification of behavioural equivalences between…
We prove that the family of solutions to vanishing viscosity approximation for multidimensional scalar conservation laws with discontinuous non-aligned flux and zero initial data in the limit generates a singular measure supported along the…
A decidability proof for bisimulation equivalence of first-order grammars is given. It is an alternative proof for a result by S\'enizergues (1998, 2005) that subsumes his affirmative solution of the famous decidability question for…
Higher-order recursion schemes are recursive equations defining new operations from given ones called "terminals". Every such recursion scheme is proved to have a least interpreted semantics in every Scott's model of \lambda-calculus in…
The rely-guarantee technique allows one to reason compositionally about concurrent programs. To handle interference the technique makes use of rely and guarantee conditions, both of which are binary relations on states. A rely condition is…
We are interested in finding a family of solutions to a singularly perturbed biharmonic equation which has a concentration behavior. The proof is based on variational methods and it is used a weak version of the Ambrosetti-Rabinowitz…
Reactive systems \`a la Leifer and Milner, an abstract categorical framework for rewriting, provide a suitable framework for deriving bisimulation congruences. This is done by synthesizing interactions with the environment in order to…