Transfer Function Synthesis without Quantifier Elimination

Traditionally, transfer functions have been designed manually for each operation in a program, instruction by instruction. In such a setting, a transfer function describes the semantics of a single instruction, detailing how a given abstract input state is mapped to an abstract output state. The net effect of a sequence of instructions, a basic block, can then be calculated by composing the transfer functions of the constituent instructions. However, precision can be improved by applying a single transfer function that captures the semantics of the block as a whole. Since blocks are program-dependent, this approach necessitates automation. There has thus been growing interest in computing transfer functions automatically, most notably using techniques based on quantifier elimination. Although conceptually elegant, quantifier elimination inevitably induces a computational bottleneck, which limits the applicability of these methods to small blocks. This paper contributes a method for calculating transfer functions that finesses quantifier elimination altogether, and can thus be seen as a response to this problem. The practicality of the method is demonstrated by generating transfer functions for input and output states that are described by linear template constraints, which include intervals and octagons.Comment: 37 pages, extended version of ESOP 2011 pape

The transfer functions of rocket nozzles

The transfer function is defined as the fractional oscillating mass flow rate divided by the fractional sinusoidal pressure oscillation in the rocket combustion chamber. This is calculated as a function of the frequency of oscillation. For very small frequencies, the transfer function is approximately 1 with a small "lead component." For very large frequencies, the transfer function is considerably larger than 1, and is approximately 1 + (γM_1)^(-1) where γ is the ratio of specific heats of the gas, and M_l is the Mach nUlllber at entrance to the nozzle

Transfer function characteristics of super resolving systems

Signal quality in an optical storage device greatly depends on the optical system transfer function used to write and read data patterns. The problem is similar to analysis of scanning optical microscopes. Hopkins and Braat have analyzed write-once-read-many (WORM) optical data storage devices. Herein, transfer function analysis of magnetooptic (MO) data storage devices is discussed with respect to improving transfer-function characteristics. Several authors have described improving the transfer function as super resolution. However, none have thoroughly analyzed the MO optical system and effects of the medium. Both the optical system transfer function and effects of the medium of this development are discussed

On determining which quantum measurement performs better for state estimation

We introduce an operational and statistically meaningful measure, the quantum tomographic transfer function, that possesses important physical invariance properties for judging whether a given informationally complete quantum measurement performs better tomographically in quantum-state estimation relative to other informationally complete measurements. This function is independent of the unknown true state of the quantum source, and is directly related to the average optimal tomographic accuracy of an unbiased state estimator for the measurement in the limit of many sampling events. For the experimentally-appealing minimally complete measurements, the transfer function is an extremely simple formula. We also give an explicit expression for this transfer function in terms of an ordered expansion that is readily computable and illustrate its usage with numerical simulations, and its consistency with some known results.Comment: 6 pages, 2 figure

Frequency-Domain Analysis of Linear Time-Periodic Systems

In this paper, we study convergence of truncated representations of the frequency-response operator of a linear time-periodic system. The frequency-response operator is frequently called the harmonic transfer function. We introduce the concepts of input, output, and skew roll-off. These concepts are related to the decay rates of elements in the harmonic transfer function. A system with high input and output roll-off may be well approximated by a low-dimensional matrix function. A system with high skew roll-off may be represented by an operator with only few diagonals. Furthermore, the roll-off rates are shown to be determined by certain properties of Taylor and Fourier expansions of the periodic systems. Finally, we clarify the connections between the different methods for computing the harmonic transfer function that are suggested in the literature

Computation of transfer function matrices of periodic systems

We present a numerical approach to evaluate the transfer function matrices of a periodic system corresponding to lifted state-space representations as constant systems. The proposed pole-zero method determines each entry of the transfer function matrix in a minimal zeros-poles- gain representation. A basic computational ingredient for this method is the extended periodic real Schur form of a periodic matrix, which underlies the computation of minimal realizations and system poles. To compute zeros and gains, fast algorithms are proposed, which are specially tailored to particular single-input single-output periodic systems. The new method relies exclusively on reliable numerical computations and is well suited for robust software implementations