Related papers: Non-Termination Sets of Simple Linear Loops
Recently Ferraris, Lee and Lifschitz proposed a new definition of stable models that does not refer to grounding, which applies to the syntax of arbitrary first-order sentences. We show its relation to the idea of loop formulas with…
This letter shows that linear Cellular Automata based on rules 90/150 generate all the solutions of linear difference equations with binary constant coefficients. Some of these solutions are pseudo-random noise sequences with application in…
A re-construction of the fundamentals of programming as a small mathematical theory (PRISM) based on elementary set theory. Highlights: $\bullet$ Zero axioms. No properties are assumed, all are proved (from standard set theory). $\bullet$ A…
Runtime verification encompasses several lightweight techniques for checking whether a system's current execution satisfies a given specification. We focus on runtime verification for Linear Temporal Logic (LTL). Previous work describes…
The chase procedure is a fundamental algorithmic tool in databases that allows us to reason with constraints, such as existential rules, with a plethora of applications. It takes as input a database and a set of constraints, and iteratively…
The paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a non strict quadratic Lyapunov function, we provide a large class of switching signals for which a…
Linear programming describes the problem of optimising a linear objective function over a set of constraints on its variables. In this paper we present a solver for linear programs implemented in the proof assistant Isabelle/HOL. This…
In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…
The set of formal power series with coefficients in an associative but noncommutative algebra becomes a loop with the substitution product. We initiate the study of this loop by describing certain Lie and Sabinin algebras related to it.…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
We exhibit assertion-preserving (reachability preserving) transformations from parameterized concurrent shared-memory programs, under a k-round scheduling of processes, to sequential programs. The salient feature of the sequential program…
Using the notion of an elementary loop, Gebser and Schaub refined the theorem on loop formulas due to Lin and Zhao by considering loop formulas of elementary loops only. In this article, we reformulate their definition of an elementary…
As demand for Real-Time applications rises among the general public, the importance of enabling large-scale, unbound algorithms to solve conventional problems with low to no latency is critical for product viability. Timer algorithms are…
Motivated by neuronal models from neuroscience, we consider the system identification of simple feedback structures whose behaviors include nonlinear phenomena such as excitability, limit-cycles and chaos. We show that output feedback is…
A system of plane curves defined by prescribing n points of multiplicity m in general position is regular if n > (2m)^2. The proof uses computation of limits of linear systems acquiring fixed divisors, an interesting problem in itself.
Linear programming (LP) relaxations are widely employed in exact solution methods for multilinear programs (MLP). One example is the family of Recursive McCormick Linearization (RML) strategies, where bilinear products are substituted for…
Applications like program synthesis sometimes require proving that a property holds for all of the infinitely many programs described by a grammar - i.e., an inductively defined set of programs. Current verification frameworks…
There are noninjective maps from surface groups to limit groups that don't kill any simple closed curves. As a corollary, there are noninjective all-loxodromic representations of surface groups to SL(2,C) that don't kill any simple closed…
We give an approximation algorithm for packing and covering linear programs (linear programs with non-negative coefficients). Given a constraint matrix with n non-zeros, r rows, and c columns, the algorithm computes feasible primal and dual…
We consider the problem of solving a linear system of equations which involves complex variables and their conjugates. We characterize when it reduces to a complex linear system, that is, a system involving only complex variables (and not…