Partition Into Triangles on Bounded Degree Graphs

We consider the Partition Into Triangles problem on bounded degree graphs. We show that this problem is polynomial-time solvable on graphs of maximum degree three by giving a linear-time algorithm. We also show that this problem becomes $\mathcal{NP}$ -complete on graphs of maximum degree four. Moreover, we show that there is no subexponential-time algorithm for this problem on graphs of maximum degree four unless the Exponential-Time Hypothesis fails. However, the Partition Into Triangles problem on graphs of maximum degree at most four is in many cases practically solvable as we give an algorithm for this problem that runs in $\mathcal{O}(1.02220^{n})$ time and linear space.     

Root-restricted Kleenean rotations

We generalize the Kleene theorem to the case where nonassociative products are used. For this purpose, we apply rotations restricted to the root of binary trees.     

Combination of convex theories: Modularity,deduction completeness,and explanation

Decision procedures are key components of theorem provers and constraint satisfaction systems. Their modular combination is of prime interest for building efficient systems, but their effective use is often limited by poor interface capabilities, when such procedures only provide a simple “sat/unsat” answer. In this paper, we develop a framework to design cooperation schemas between such procedures while maintaining modularity of their interfaces. First, we use the framework to specify and prove the correctness of classic combination schemas by Nelson–Oppen and Shostak. Second, we introduce the concept of deduction complete satisfiability procedures, we show how to build them for large classes of theories, then we provide a schema to modularly combine them. Third, we consider the problem of modularly constructing explanations for combinations by re-using available proof-producing procedures for the component theories.     

Regaining cut admissibility in deduction modulo using abstract completion

Deduction modulo is a way to combine computation and deduction in proofs, by applying the inference rules of a deductive system (e.g. natural deduction or sequent calculus) modulo some congruence that we assume here to be presented by a set of rewrite rules. Using deduction modulo is equivalent to proving in a theory corresponding to the rewrite rules, and leads to proofs that are often shorter and more readable. However, cuts may be not admissible anymore.We define a new system, the unfolding sequent calculus, and prove its equivalence with the sequent calculus modulo, especially w.r.t. cut-free proofs. It permits to show that it is even undecidable to know if cuts can be eliminated in the sequent calculus modulo a given rewrite system.Then, to recover the cut admissibility, we propose a procedure to complete the rewrite system such that the sequent calculus modulo the resulting system admits cuts. This is done by generalizing the Knuth–Bendix completion in a non-trivial way, using the framework of abstract canonical systems.These results enlighten the entanglement between computation and deduction, and the power of abstract completion procedures. They also provide an effective way to obtain systems admitting cuts, therefore extending the applicability of deduction modulo in automated theorem proving.     

Stream engines meet wireless sensor networks: cost-based planning and processing of complex queries in AnduIN

Wireless sensor networks are powerful, distributed, self-organizing systems used for event and environmental monitoring. In-network query processors like TinyDB offer a user friendly SQL-like application development. Due to the sensor nodes?? resource limitations, monolithic approaches often support only a restricted number of operators. For this reason, complex processing is typically outsourced to the base station. Nevertheless, previous work has shown that complete or partial in-network processing can be more efficient than the base station approach. In this paper, we introduce AnduIN, a system for developing, deploying, and running complex in-network processing tasks. In particular, we present the query planning and execution strategies used in AnduIN, a system combining sensor-local in-network processing and a data stream engine. Query planning employs a multi-dimensional cost model taking energy consumption into account and decides autonomously which query parts will be processed within the sensor network and which parts will be processed at the central instance.     

Comprehensive Automation for Specialty Crops: Year 1 results and lessons learned

Comprehensive Automation for Specialty Crops is a project focused on the needs of the specialty crops sector, with a focus on apples and nursery trees. The project’s main thrusts are the integration of robotics technology and plant science; understanding and overcoming socio-economic barriers to technology adoption; and making the results available to growers and stakeholders through a nationwide outreach program. In this article, we present the results obtained and lessons learned in the first year of the project with a reconfigurable mobility infrastructure for autonomous farm driving. We then present sensor systems developed to enable three real-world agricultural applications—insect monitoring, crop load scouting, and caliper measurement—and discuss how they can be deployed autonomously to yield increased production efficiency and reduced labor costs.     

On the relationship between subjective and objective measures of fatigue

Objective: Objective and subjective methods have been used in the past to assess workplace fatigue, but little is known about correlations between them. We examine correlations between subjective and objective measures, including measures collected in a workplace scenario. Methods: 15 young and 17 older participants were assessed before and after work with four types of fatigue measure: objective physical (posturography), objective mental (psychomotor vigilance task), subjective physical and mental (self-assessment), objective and subjective realistic (oculomotor behaviour, observer-rated facial expression, typing performance). Results: Pre- and post-test scores were analysed with an ANOVA, significant differences were submitted to a factor analysis. It yielded three factors: one representing posturography, the second self-rated mental and physical fatigue and the third observer-rated facial expression. Conclusions: Results advocate the existence of three independent fatigue components: Objective physical fatigue, introspective and extrospective fatigue.

Practitioner Summary: This study analyses correlations between different subjective and objective fatigue markers to better understand the complex nature of workplace fatigue. Measurements were conducted directly at the workplace. Results reveal that fatigue comprises three independent fatigue components: Objective physical fatigue, introspective and extrospective fatigue.     

A Newton-like finite element scheme for compressible gas flows

Semi-implicit and Newton-like finite element methods are developed for the stationary compressible Euler equations. The Galerkin discretization of the inviscid fluxes is potentially oscillatory and unstable. To suppress numerical oscillations, the spatial discretization is performed by a high-resolution finite element scheme based on algebraic flux correction. A multidimensional limiter of TVD type is employed. An important goal is the efficient computation of stationary solutions in a wide range of Mach numbers, which is a challenging task due to oscillatory correction factors associated with TVD-type flux limiters. A semi-implicit scheme is derived by a time-lagged linearization of the nonlinear residual, and a Newton-like method is obtained in the limit of infinite CFL numbers. Special emphasis is laid on the numerical treatment of weakly imposed characteristic boundary conditions. Numerical evidence for unconditional stability is presented. It is shown that the proposed approach offers higher accuracy and better convergence behavior than algorithms in which the boundary conditions are implemented in a strong sense.     

Verifying a Network Invariant for All Configurations of the Futurebus+ Cache Coherence Protocol

In this paper we describe a network invariant for all configurations of the Futurebus+ Cache Coherence Protocol. The network invariant was computed with PAX and verified by a model checker. Using this invariant we are able to prove a specification of cache coherence correct for an arbitrary number of components on a single bus of the system. This specification includes a progress property not proven yet. We show how the result for the single bus system can be extended to tree-shaped systems. This is, as far as we know, the first uniform proof of the protocol with multiple data-buses.