A Comparison of Free BDDs and Transformed BDDs

Ordered binary decision diagrams (OBDDs) introduced by Bryant (IEEE Trans. on Computers, Vol. 35, pp. 677–691, 1986) have found a lot of applications in verification and CAD. Their use is limited if the OBDD size of the considered functions is too large. Therefore, a variety of generalized BDD models has been presented, among them FBDDs (free BDDs) and TBDDs (transformed BDDs). Here the quite tight relations between these models are revealed and their advantages and disadvantages are discussed.     

A note on classes of complements and the LBA problem

Summary The complements of an AFL form an AFL if and only if is closed under length-preserving universal quantification. The complements of the context-sensitive languages form a principal AFL with a hardest set L ₁. The context-sensitive languages are closed under complementation if and only if L ₁ is context-sensitive.This research was supported in part by the National Science Foundation under Grants MCS76-10076 and DCR74-15091     

Amounts of nondeterminism in finite automata

Summary The amount of nondeterminism in a nondeterministic finite automaton (NFA) is measured by counting the minimal number of guessing points a string w has to pass through on its way to an accepting state. NFA's with more nondeterminism can achieve greater savings in the number of states over their deterministic counterparts than NFA's with less nondeterminism. On the other hand, for some nontrivial infinite regular languages a deterministic finite automaton (DFA) can already be quite succinct in the sense that NFA's need as many states (and even context-free grammars need as many nonterminals) as the minimal DFA has states.This research was supported in part by the National Science Foundation under Grant No. MCS 76-10076     

On reducing the number of states in a PDA

A transformation is presented which converts any pushdown automaton (PDA)M ₀ withn ₀ states andp ₀ stack symbols into an equivalent PDAM withn states and n ₀ /n² p ₀ stack symbols into an equivalent ofn, 1n ₀. This transformation preserves realtime behavior but not derterminism. The transformation is proved to be the best possible one in the following sense: for each choice of the parametersn ₀ + 1 stack symbols for any desired value realtime PDAM ₀ such that any equivalent PDAM (whether realtime or not) havingn states must have at least (n ₀ /n)² p₀ stack symbols. Furthermore, the loss of deterministic behavior cannot be avoided, since for each choice ofn ₀ andp ₀, there is a deterministic PDAM ₀ such that no equivalent PDAM with fewer states can be deterministic.This research was supported in part by the National Science Foundation under Grants MCS76-10076 and MCS76-10076A01.     

Temperature stability of thin anodic oxide films in metal/insulator/metal structures: A comparison between tantalum and aluminium oxide

The dielectric breakdown of thin (d = 3–4 nm) aluminium and tantalum oxide films was investigated by means of current voltage plots in metal/insulator/metal systems. Dielectric breakdown field strengths, E_DB, of 0.6 GV m^− 1 were found for both oxide types at room temperature. Differences appear in the temperature dependence of E_DB. Tantalum oxide films show an unchanged breakdown behaviour for temperatures up to 420 K while aluminium oxide films lose already 80% of their E_DB value in the same temperature range. Time-resolved investigations of the electric breakdown revealed intermediate states of both oxide types which were stable for several ms being characterized by an enhanced tunnel current. The breakdown voltage clearly scales with the oxide thickness for both oxide types.     

On measuring nondeterminism in regular languages

It is well known that allowing nondeterminism in a finite automaton can produce in the most extreme case an exponential savings in the number of states required to recognize a regular language. This paper studies situations intermediate between forbidding nondeterminism and allowing it. The amount of nondeterminism used by a finite automaton is quantified, so that the decrease in the size of the state space that occurs as the amount of nondeterminism that is permitted increases in increments can be studied. These intermediate situations are shown always to lie between two extremes:(1) there are no savings as the amount of nondeterminism increases incrementally, so that savings occur only when the amount of nondeterminism becomes unlimited;(2) each increment of nondeterminism results in additional savings, the number s of states decreasing approximately as s^1/i, until exponential savings have been achieved after about i = logs/log log s increments.