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A Letter from the Outgoing Editor of IJNS
Dr. Russel Hirst says farewell to his time as Managing Editor at IJNS
Archway Commencement Issue, v. 19, no. 18, July 11, 1958
Archway v. 19, no. 18, July 11, 1958 - Commencement issue
Compressed Membership for NFA (DFA) with Compressed Labels is in NP (P)
In this paper, a compressed membership problem for finite automata, both
deterministic and non-deterministic, with compressed transition labels is
studied. The compression is represented by straight-line programs (SLPs), i.e.
context-free grammars generating exactly one string. A novel technique of
dealing with SLPs is introduced: the SLPs are recompressed, so that substrings
of the input text are encoded in SLPs labelling the transitions of the NFA
(DFA) in the same way, as in the SLP representing the input text. To this end,
the SLPs are locally decompressed and then recompressed in a uniform way.
Furthermore, such recompression induces only small changes in the automaton, in
particular, the size of the automaton remains polynomial.
Using this technique it is shown that the compressed membership for NFA with
compressed labels is in NP, thus confirming the conjecture of Plandowski and
Rytter and extending the partial result of Lohrey and Mathissen; as it is
already known, that this problem is NP-hard, we settle its exact computational
complexity. Moreover, the same technique applied to the compressed membership
for DFA with compressed labels yields that this problem is in P; for this
problem, only trivial upper-bound PSPACE was known
On-line construction of position heaps
We propose a simple linear-time on-line algorithm for constructing a position
heap for a string [Ehrenfeucht et al, 2011]. Our definition of position heap
differs slightly from the one proposed in [Ehrenfeucht et al, 2011] in that it
considers the suffixes ordered from left to right. Our construction is based on
classic suffix pointers and resembles the Ukkonen's algorithm for suffix trees
[Ukkonen, 1995]. Using suffix pointers, the position heap can be extended into
the augmented position heap that allows for a linear-time string matching
algorithm [Ehrenfeucht et al, 2011].Comment: to appear in Journal of Discrete Algorithm
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