It it shown that the first-order theory of an automatic structure, whose Gaifman graph has bounded degree, is decidable in doubly exponential space (for injective automatic presentations, this holds even uniformly). Presenting an automatic structure of bounded degree whose theory is hard for 2EXPSPACE, we also prove this result to be optimal. These findings close the gap left open in [14].

We show that Zilber’s conjecture that complex exponentiation is isomorphic to his pseudo-exponentiation follows from the a priori simpler conjecture that they are elementarily equivalent. An analysis of the firstorder types in pseudo-exponentiation leads to a description of the elementary embeddings, and the result that pseudo-exponential fields are precisely the models of their common first-or...

PID Controller is used for tuning of three constants (P,I&D).It stabilize the system by reducing oscillations and settling time. In the proposed method, new tuning rules based on the exact satisfaction of gain and phase margin specifications using proportional-integral (PI) and proportional-integral-differential (PID) type controllers are used for unstable first-order plus dead-time (UFOPDT) pr...

This paper presents a novel First Order Plus Fractional Diffusive Delay (FOPFDD) model, capable of modeling delay dominant systems with high accuracy. The novelty the FOPFDD is (FDD) term, an exponential non-integer order $\alpha$, i.e. $e^{-(Ls)^{\alpha}}$ in Laplace domain. special cases $\alpha = 0.5$ and 1$ have already been investigated thoroughly. In this work $\alpha$ generalized to any ...

A function of boolean arguments is symmetric if its value depends solely on the number of l 's among its arguments. In the first part of this paper we partially characterize those symmetric functions that can be computed by constant-depth polynomial-size sequences of boolean circuits, and discuss the complete characterization. (We treat both uniform and non-uniform sequences of circuits.) Our r...