1,000 research outputs found
A Note on Nested String Replacements
We investigate the number of nested string replacements required to reduce a
string of identical characters to one character
A Non-Oblivious Reduction of Counting Ones to Multiplication
An algorithm counting the number of ones in a binary word is presented
running in time where is the number of ones. The operations
available include bit-wise logical operations and multiplication
Some Remarks on Real-Time Turing Machines
The power of real-time Turing machines using sublinear space is investigated.
In contrast to a claim appearing in the literature, such machines can accept
non-regular languages, even if working in deterministic mode. While maintaining
a standard binary counter appears to be impossible in real-time, we present a
guess and check approach that yields a binary representation of the input
length. Based on this technique, we show that unary encodings of languages
accepted in exponential time can be recognized by nondeterministic real-time
Turing machines
On Practical Regular Expressions
We report on simulation, hierarchy, and decidability results for Practical
Regular Expressions (PRE), which may include back references in addition to the
standard operations union, concatenation, and star.
The following results are obtained:
PRE can be simulated by the classical model of nondeterministic finite
automata with sensing one-way heads. The number of heads depends on the number
of different variables in the expressions.
A space bound O(n log m) for matching a text of length m with a PRE with n
variables based on the previous simulation. This improves the bound O(nm) from
(C\^ampeanu and Santean 2009).
PRE cannot be simulated by deterministic finite automata with at most three
sensing one-way heads or deterministic finite automata with any number of
non-sensing one-way heads.
PRE with a bounded number of occurrences of variables in any match can be
simulated by nondeterministic finite automata with one-way heads.
There is a tight hierarchy of PRE with a growing number of non-nested
variables over a fixed alphabet. A previously known hierarchy was based on
nested variables and growing alphabets (Larsen 1998).
Matching of PRE without star over a single-letter alphabet is NP-complete.
This strengthens the corresponding result for expressions over larger alphabets
and with star (Aho 1990).
Inequivalence of PRE without closure operators is Sigma^P_2-complete.
The decidability of universality of PRE over a single letter alphabet is
linked to the existence of Fermat Primes.
Greibach's Theorem applies to languages characterized by PRE
A SWAR Approach to Counting Ones
We investigate the complexity of algorithms counting ones in different sets
of operations. With addition and logical operations (but no shift)
steps suffice to count ones. Parity can be computed with
complexity , which is the same bound as for methods using
shift-operations. If multiplication is available, a solution of time complexity
is possible improving the known bound
Counting Ones Without Broadword Operations
A lower time bound for counting the number of
ones in a binary input word of length is presented, where is
the number of ones. The operations available are increment, decrement, bit-wise
logical operations, and assignment. The only constant available is zero. An
almost matching upper bound is also obtained
An NL-Complete Puzzle
We investigate the complexity of a puzzle that turns out to be NL-complete
Efficient Computation by Three Counter Machines
We show that multiplication can be done in polynomial time on a three counter
machine that receives its input as the contents of two counters. The technique
is generalized to functions of two variables computable by deterministic Turing
machines in linear space
Some Remarks on Lower Bounds for Queue Machines (Preliminary Report)
We first give an improved lower bound for the deterministic online simulation
of tapes or pushdown stores by queues. Then we inspect some proofs in a
classical work on queue machines in the area of Formal Languages and outline
why a main argument in the proofs is incomplete. Based on descriptional
complexity, we show the intuition behind the argument to be correct
The Complexity of Some Combinatorial Puzzles
We show that the decision versions of the puzzles Knossos and The Hour-Glass
are complete for NP
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