Lower Bounds on the Size of Quantum Automata Accepting Unary Languages

2003 ◽  
pp. 86-96 ◽  
Author(s):  
Alberto Bertoni ◽  
Carlo Mereghetti ◽  
Beatrice Palano
Keyword(s):  
Lower Bounds ◽  
Quantum Automata ◽  
Unary Languages

scholarly journals Size lower bounds for quantum automata

2014 ◽  
Vol 551 ◽  
pp. 102-115 ◽  
Author(s):  
Maria Paola Bianchi ◽  
Carlo Mereghetti ◽  
Beatrice Palano
Keyword(s):  
Lower Bounds ◽  
Quantum Automata

Size Lower Bounds for Quantum Automata

2013 ◽  
pp. 19-30 ◽  
Author(s):  
Maria Paola Bianchi ◽  
Carlo Mereghetti ◽  
Beatrice Palano
Keyword(s):  
Lower Bounds ◽  
Quantum Automata

SIMULATIONS OF UNARY ONE-WAY MULTI-HEAD FINITE AUTOMATA

2014 ◽  
Vol 25 (07) ◽  
pp. 877-896 ◽  
Author(s):  
MARTIN KUTRIB ◽  
ANDREAS MALCHER ◽  
MATTHIAS WENDLANDT
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Finite Automaton ◽  
Finite Automata ◽  
Upper And Lower Bounds ◽  
Unary Languages ◽  
Order Of Magnitude ◽  
Simulation Results ◽  
Special Case ◽  
Nondeterministic Finite Automaton

We investigate the descriptional complexity of deterministic one-way multi-head finite automata accepting unary languages. It is known that in this case the languages accepted are regular. Thus, we study the increase of the number of states when an n-state k-head finite automaton is simulated by a classical (one-head) deterministic or nondeterministic finite automaton. In the former case upper and lower bounds that are tight in the order of magnitude are shown. For the latter case we obtain an upper bound of O(n2k) and a lower bound of Ω(nk) states. We investigate also the costs for the conversion of one-head nondeterministic finite automata to deterministic k-head finite automata, that is, we trade nondeterminism for heads. In addition, we study how the conversion costs vary in the special case of finite and, in particular, of singleton unary lanuages. Finally, as an application of the simulation results, we show that decidability problems for unary deterministic k-head finite automata such as emptiness or equivalence are LOGSPACE-complete.

TESTING THE DESCRIPTIONAL POWER OF SMALL TURING MACHINES ON NONREGULAR LANGUAGE ACCEPTANCE

2008 ◽  
Vol 19 (04) ◽  
pp. 827-843 ◽  
Author(s):  
CARLO MEREGHETTI
Keyword(s):  
Lower Bounds ◽  
Turing Machines ◽  
Unary Languages ◽  
Alternating Turing Machines

We study lower bounds on space and input head reversals for deterministic, nondeterministic, and alternating Turing machines accepting nonregular languages. Three notions of space, namely strong, middle, weak are considered, and another notion, called accept, is introduced. In all cases, we obtain tight lower bounds. Moreover, we show that, while for determinism and nondeterminism such lower bounds are optimal even with respect to unary languages, for alternation optimal lower bounds for unary languages turn out to be strictly higher than those for languages over alphabets with two or more symbols.

Lower Bounds in Communication Complexity

2007 ◽  
Author(s):  
T. Lee ◽  
A. Shraibman
Keyword(s):  
Lower Bounds ◽  
Communication Complexity

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base
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