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Complexity of Normal Form Properties and Reductions for Term Rewriting Problems

Verma R.

Fundamenta Informaticae

2009

Vol. 92, nr 1-2

145-168

We present several new and some significantly improved polynomial-time reductions between basic decision problems of term rewriting systems. We prove two theorems that imply tighter upper bounds for deciding the uniqueness of normal forms (UN^=) and unique normalization (UN^&rar;) properties under certain conditions. From these theorems we derive a new and simpler polynomial-time algorithm for the UN^= property of ground rewrite systems, and explicit upper bounds for both UN^= and UN! properties of left-linear right-ground systems. We also show that both properties are undecidable for right-ground systems. It was already known that these properties are undecidable for linear systems. Hence, in a sense the decidability results are "close" to optimal.

Electron beam irradiation induced changes in liquid-crystal compound 5CB

Rath M. C., Sarkar S. K., Wadhawan V. K., Verma R., Das I. M. L., Dąbrowski R., Tykarska M., Dhar R.

Opto-Electronics Review

2008

Vol. 16, No. 4

399-403

Electron beam irradiation studies on liquid crystal material 5CB have been carried out at a temperature where the compound exists in the isotropic liquid phase. In situ time-resolved spectroscopic characterization was carried out during the irradiation. Three different transients were observed during the 2-μs electron pulse. After about 50 μs, only one transient species was found to be present, which has an absorption peak at 360 nm. Radiolysed sample exhibits a broad absorption at ∼ 400 nm. The dielectric measurements show that even a low level of irradiation results in a dramatic increase in the component of dielectric permittivity normal to the long axes of the molecules ε ⊥', and a corresponding decrease in the dielectric anisotropy (Δ ε'=ε II — ε ⊥'). These studies show that 5CB is prone to substantial radiation damage on exposure to the beam of high-energy electrons.