Space bounded computations: review and new separation results
MFCS '89 Selected papers of the symposium on Mathematical foundations of computer science
ASPACE(o(log log n)) is regular
SIAM Journal on Computing
Bits and relative order from residues, space efficiently
Information Processing Letters
The Sublogarithmic Alternating Space World
SIAM Journal on Computing
Bridging across the log (n) space frontier
Information and Computation
Journal of the ACM (JACM)
Number Theory for Computing
Turing Machines with Sublogarithmic Space
Turing Machines with Sublogarithmic Space
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Space Bounded Computations: Review And New Separation Results
MFCS '89 Proceedings on Mathematical Foundations of Computer Science 1989
Introduction to Automata Theory, Languages, and Computation
Introduction to Automata Theory, Languages, and Computation
Factoring and Testing Primes in Small Space
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
Hi-index | 0.00 |
(i) There exists an NP-complete language $\mathcal{L}$ such that its unary coded version un-$\mathcal{L}$ is in ASpace(log log n). (ii) If P ≠ NP, there exists a binary language $\mathcal{L}$ such that its unary version un-$\mathcal{L}$ is in ASpace(log log n), while the language $\mathcal{L}$ itself is not in ASpace(log n). As a consequence, under assumption that P ≠ NP, the standard space translation between unary and binary languages does not work for alternating machines with small space, the equivalence $\mathcal{L} \in$ ASpace(s(n)) ≡ un-$\mathcal{L} \in$ ASpace(s(log n)) is valid only if s(n)∈Ω(n). This is quite different from deterministic and nondeterministic machines, for which the corresponding equivalence holds for each s(n)∈Ω(log n), and hence for s(log n)∈Ω(log log n).