State reduction of incompletely specified finite sequential machines

Bu çalışmada, kısmen belirli ardışıl makinelerde durum indirgeme konusu ele alınmıştır. Durum indirgeme için geliştirilen algoritmalar, Boole fonksiyonlarının birlikte indirgenmesi, durum kodlama ve tek koşullu örtü problemi çözme gibi lojik tasarımın diğer adımlarına da uygulanmıştır. Bu çalışmada kullanılan kapalı yollar kümesi kavramına ve bu kümeden minimal kapalı örtü elde etmeye dayanan bir yönteme literatürde rastlanmamıştır. Bu algoritmalara dayanan, SRC (State Reduction and Covering) programı geliştirilmiştir. SRC, MCNC ve diğer bençmarklarda Rho yöntemi (Rho vd., 1994) ve Puri yöntemi (Puri ve Gu, 1993) ile karşılaştırılmıştır. Test sonuçlarından da görüldüğü gibi SRC programı özellikle kritik bençmarklarda daha iyi sonuç vermiştir.Anahtar Kelimeler: lojik tasarım, algoritma, durum indirgeme, örtü problemi.This paper is concerned with the problem of synthesizing a class of digital circuits, sequential circuits, more specifically state reduction of of incompletely specified sequential circuits. State reduction is an important step in the design of the synchronous and asynchronous sequential circuits. The algorithms which are developed for state reduction, are also applied to other steps of the logic synthesis, such as multiple-output Boolean minimization, state encoding and unite/binate covering problems. In this paper three algorithms are presented to find a minimal equivalent of a given incompletely specified finite sequential machine. These algorithms use a new concept; closed paths constituted by compatibles or prime compatibles. This closed paths concept and an algorithm which uses this concept is not observed in the literature. These algorithms are implemented in an efficient computer program SRC (State Reduction and Covering). SRC is run and tested on several FSMs including the MCNC FSM benchmarks and the results are given in conclusion. From the test results, it can be seen that, despite of the limited computing resources, SRC is more efficient on all benchmarks, especially on the critical benchmarks. Using these algorithms, MORP (Multiple Output Reduction Program) developed to realize m Boolean functions with n variables. State reduction methods which are developed in this work, are also applied to state encoding problem and a computer program, OPASKOD (Race-free State Assignment Program) developed.Keywords: logic synthesis, algorithm, state reduction, covering problem

The dynamical mass and evolutionary status of the type-II Cepheid in the eclipsing binary system OGLE-LMC-T2CEP-211 with a double-ring disk

We present the analysis of a peculiar W~Virginis (pWVir) type-II Cepheid, OGLE-LMC-T2CEP-211 ($P_{puls}=9.393\,d$), in a double-lined binary system ($P_{orb}=242\,d$), which shed light on virtually unknown evolutionary status and structure of pWVir stars. The dynamical mass of the Cepheid (first ever for a type-II Cepheid) is $0.64\pm{}0.02\,M_\odot$ and the radius $R=25.1\pm{}0.3\,R_\odot$. The companion is a massive ($5.67\,M_\odot$) main-sequence star obscured by a disk. Such configuration suggests a mass transfer in the system history. We found that originally the system ($P_{orb}^{init}=12\,d$) was composed of $3.5$ and $2.8\,M_\odot$ stars, with the current Cepheid being more massive. The system age is now $\sim{}$200 My, and the Cepheid is almost completely stripped of hydrogen, with helium mass of $\sim{}92\%$ of the total mass. It finished transferring the mass 2.5 My ago and is evolving towards lower temperatures passing through the instability strip. Comparison with observations indicate a reasonable $2.7\cdot{}10^{-8}\,M_\odot/y$ mass loss from the Cepheid. The companion is most probably a Be main-sequence star with $T=22000\,K$ and $R=2.5\,R_\odot$. Our results yield a good agreement with a pulsation theory model for a hydrogen-deficient pulsator, confirming the described evolutionary scenario. We detected a two-ring disk ($R_{disk}\sim\,116\,R_{\odot}$) and a shell ($R_{shell}\sim\,9\,R_{\odot}$) around the companion, that is probably a combination of the matter from the past mass transfer, the mass being lost by the Cepheid due to wind and pulsations, and a decretion disk around a rapidly rotating secondary. Our study together with observational properties of pWVir stars suggests that their majority are products of a similar binary evolution interaction.Comment: 21 pages, 14 figures, 6 tables, accepted for publication in Ap

Absolute properties of the neglected eclipsing B-type binary HD 194495

We present the results of the high-resolution spectroscopic observations of the neglected binary system HD\,194495 (B3\,IV-V+B4\,V). A combined analysis of three different photometric data set ($Tycho$ B$_T$ and V$_T$ photometry, H$_p$-band data of $Hipparcos$ and $V-$band data of ASAS3 photometry) and radial velocities indicates that the system has an orbital period of 4.90494 $\pm$ 0.00005 days and an inclination of 69$\pm$1 degrees. This solution yields masses and radii of $M_{\rm 1}$ = 7.57$\pm$0.08 $M_{\odot}$ and $R_{\rm 1}$ = 5.82$\pm$0.03 $R_{\odot}$ for the primary and $M_{\rm 2}$ = 5.46$\pm$0.09 $M_{\odot}$ and $R_{\rm 2}$ = 3.14$\pm$0.08 $R_{\odot}$ for the secondary. Based on the position of the two stars plotted on a theoretical H-R diagram, we find that the age of the system is $\gtrsim$ 28 Myr, according to stellar evolutionary models. The spectroscopic and photometric results are in agreement with those obtained using theoretical predictions.Comment: 17 pages, 5 figures, 5 tables; New Astronomy, 201