Achievable High Scores of epsilon-Moves and Running Times in DPDA Computations

Large scores in the number of e-moves a DPDA can make without entering a loop or decreasing its stack below the original stack height are investigated. The achieved scores are very near to an upper bound in the general case and are the upper bound for one-state DPDA’s. Upper and lower bounds are derived for the worst case running times of accepting DPDA computations. Hence, given an arbitrary (non looping) DPDA, we have a priori right upper and lower bounds on how inefficient its computations can be in the wprst case. As will appear. these bounds do not follow straightaway from the largest amount of concezutive e-moves a DPDA with given parameters can make in the worst case, since it may use a stacking and popping regime of e-moves and read moves in an ingeneous way. Deterministic pushdown automata (DADA ‘s) accept the so-called deterministic context free languages and constitute an important device in the theory of parsing and compiling [ 11. Given a DPDA acceptor for some language (the device tells us whether an input word is in the language) we can convert it to a recognizer (the device tells us whether or not the input word is in the language) by eliminating loops, i.e., infinite sequences of consecutive E-moves (nonreading machine steps). Schiitzenberger [5] showed how one can do so. kdter proofs analyzed the amount of work involved in bringing a DPDA in loop-free form, which involved giving an upper bound on the