1,269 research outputs found
Trading Determinism for Time in Space Bounded Computations
Savitch showed in that nondeterministic logspace (NL) is contained in
deterministic space but his algorithm requires
quasipolynomial time. The question whether we can have a deterministic
algorithm for every problem in NL that requires polylogarithmic space and
simultaneously runs in polynomial time was left open.
In this paper we give a partial solution to this problem and show that for
every language in NL there exists an unambiguous nondeterministic algorithm
that requires space and simultaneously runs in
polynomial time.Comment: Accepted in MFCS 201
One-Tape Turing Machine Variants and Language Recognition
We present two restricted versions of one-tape Turing machines. Both
characterize the class of context-free languages. In the first version,
proposed by Hibbard in 1967 and called limited automata, each tape cell can be
rewritten only in the first visits, for a fixed constant .
Furthermore, for deterministic limited automata are equivalent to
deterministic pushdown automata, namely they characterize deterministic
context-free languages. Further restricting the possible operations, we
consider strongly limited automata. These models still characterize
context-free languages. However, the deterministic version is less powerful
than the deterministic version of limited automata. In fact, there exist
deterministic context-free languages that are not accepted by any deterministic
strongly limited automaton.Comment: 20 pages. This article will appear in the Complexity Theory Column of
the September 2015 issue of SIGACT New
Space hierarchy theorem revised
AbstractWe show that, for an arbitrary function h(n) and each recursive function ℓ(n), that are separated by a nondeterministically fully space constructible g(n), such that h(n)∈Ω(g(n)) but ℓ(n)∉Ω(g(n)), there exists a unary language L in NSPACE(h(n)) that is not contained in NSPACE(ℓ(n)). The same holds for the deterministic case.The main contribution to the well-known Space Hierarchy Theorem is that (i) the language L separating the two space classes is unary (tally), (ii) the hierarchy is independent of whether h(n) or ℓ(n) are in Ω(logn) or in o(logn), (iii) the functions h(n) or ℓ(n) themselves need not be space constructible nor monotone increasing, (iv) the hierarchy is established both for strong and weak space complexity classes. This allows us to present unary languages in such complexity classes as, for example, NSPACE(loglogn·log∗n)⧹NSPACE(loglogn), using a plain diagonalization
Communication complexity and combinatorial lattice theory
AbstractIn a recent paper, Hajnal, Maass, and Turán analyzed the communication complexity of graph connectivity. Building on this work, we develop a general framework for the study of a broad class of communication problems which has several interesting special cases including the graph connectivity problem. The approach is based on the combinatorial theory of alignments and lattices
History-Register Automata
Programs with dynamic allocation are able to create and use an unbounded
number of fresh resources, such as references, objects, files, etc. We propose
History-Register Automata (HRA), a new automata-theoretic formalism for
modelling such programs. HRAs extend the expressiveness of previous approaches
and bring us to the limits of decidability for reachability checks. The
distinctive feature of our machines is their use of unbounded memory sets
(histories) where input symbols can be selectively stored and compared with
symbols to follow. In addition, stored symbols can be consumed or deleted by
reset. We show that the combination of consumption and reset capabilities
renders the automata powerful enough to imitate counter machines, and yields
closure under all regular operations apart from complementation. We moreover
examine weaker notions of HRAs which strike different balances between
expressiveness and effectiveness.Comment: LMCS (improved version of FoSSaCS
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