Positive modal algebras are the $$\left\langle { \wedge , \vee ,\diamondsuit ,\square,0,1} \right\rangle $$-subreducts of modal algebras. We prove that the variety of positive S4-algebras is not locally finite. On the other hand, the free one-generated positive S4-algebra is shown to be finite. Moreover, we describe the bottom part of the lattice of varieties of positive S4-algebras. Building on this, we characterize (passively, hereditarily) structurally complete varieties of positive K4-algebras.

This paper presents a neural network-based four-direction search scheme of path planning for mobile agents, given a known environmental map with stationary obstacles. Firstly, the map collision energy is modeled for all the obstacles based on neural network. Secondly, for the shorted path-search purpose, the path energy is considered. Thirdly, to decrease the path-search time, a variable step-length is designed with respect to collision energy of the previous iteration path. Simulation results demonstrate that the variable step-length is effective and can decrease the iteration time substantially. Lastly, experimental results show that the mobile agent tracks the generated path well. Both the simulation and experiment results substantiate the feasibility and realizability of the presented scheme.

The effect of signals on stability, stable throughput region, and delay in a two-user slotted ALOHA-based random-access system with collisions is considered. This work gives rise to the development of random access G-networks, which can model security attacks, expiration of deadlines, or other malfunctions, and introduce load balancing among highly interacting queues. The users are equipped with infinite capacity buffers accepting external bursty arrivals. We consider both negative and triggering signals. Negative signals delete a packet from a user queue, while triggering signals cause the instantaneous transfer of packets among user queues. We obtain the exact stability region, and show that the stable throughput region is a subset of it. Moreover, we perform a compact mathematical analysis to obtain exact expressions for the queueing delay by solving a non-homogeneous Riemann boundary value problem. A computationally efficient way to obtain explicit bounds for the expected number of buffered packets at user queues is also presented. The theoretical findings are numerically evaluated and insights regarding the system performance are derived.

We analyze Energy Packet Networks (EPNs) in which the service centers consist of multiclass queues and the Data Packets (DPs) initiate the transfer (i.e., the arrival of a DP at the battery triggers the movement) with multiple energy packet requirements. In other words, a class-k DP in cell i is sent successfully to the next cell if there are $c_i^{(k)}$ energy packets and it is dropped otherwise. Besides, we consider that the queues handling DPs operate under one of the following disciplines: First-Input-First-Output (FIFO), Processor Sharing (PS), or Preemptive Last-Input-First-Output (LIFO-PR). This model is an extension of previously studied EPNs [6,16] where the steady-state distribution of the number of jobs in the queues has a product form. In our model, we show the existence of a product form of the steady-state stationary distribution, where the load of the servers is given by a fixed point expression. We study the existence of a solution to the derived fixed point problem and we provide sufficient conditions for the stability of our model. Finally, we show that, for feed forward EPNs, the load of all the queues can be fully characterized.

This article investigates the proof theory of the Quantified Argument Calculus (Quarc) as developed and systematically studied by Hanoch Ben-Yami [3, 4]. Ben-Yami makes use of natural deduction (Suppes-Lemmon style), we, however, have chosen a sequent calculus presentation, which allows for the proofs of a multitude of significant meta-theoretic results with minor modifications to the Gentzen’s original framework, i.e., LK. As will be made clear in course of the article LK-Quarc will enjoy cut elimination and its corollaries (including subformula property and thus consistency).