63 research outputs found
Finite state verifiers with constant randomness
We give a new characterization of as the class of languages
whose members have certificates that can be verified with small error in
polynomial time by finite state machines that use a constant number of random
bits, as opposed to its conventional description in terms of deterministic
logarithmic-space verifiers. It turns out that allowing two-way interaction
with the prover does not change the class of verifiable languages, and that no
polynomially bounded amount of randomness is useful for constant-memory
computers when used as language recognizers, or public-coin verifiers. A
corollary of our main result is that the class of outcome problems
corresponding to O(log n)-space bounded games of incomplete information where
the universal player is allowed a constant number of moves equals NL.Comment: 17 pages. An improved versio
Superiority of one-way and realtime quantum machines and new directions
In automata theory, the quantum computation has been widely examined for
finite state machines, known as quantum finite automata (QFAs), and less
attention has been given to the QFAs augmented with counters or stacks.
Moreover, to our knowledge, there is no result related to QFAs having more than
one input head. In this paper, we focus on such generalizations of QFAs whose
input head(s) operate(s) in one-way or realtime mode and present many
superiority of them to their classical counterparts. Furthermore, we propose
some open problems and conjectures in order to investigate the power of
quantumness better. We also give some new results on classical computation.Comment: A revised edition with some correction
Automata with modulo counters and nondeterministic counter bounds
We introduce and investigate Nondeterministically Bounded
Modulo Counter Automata (NBMCA), which are two-way one-head automata
that comprise a constant number of modulo counters, where the
counter bounds are nondeterministically guessed, and this is the only
element of nondeterminism. NBMCA are tailored to recognising those
languages that are characterised by the existence of a specific factorisation
of their words, e. g., pattern languages. In this work, we subject
NBMCA to a theoretically sound analysis
Tradeoffs for language recognition on alternating machines
AbstractThe alternating machine having a separate input tape with k two-way, read-only heads, and a certain number of internal configurations, AM(k), is considered as a parallel computing model. For the complexity measure TIME · SPACE · PARALLELISM (TSP), the optimal lower bounds Ω(n2) and Ω(n3/2) respectively are proved for the recognition of specific languages on AM(1) and AM(k) respectively. For the complexity measure REVERSALS · SPACE · PARALLELISM (RSP), the lower bound Ω(n1/2) is established for the recognition of a specific language on AM(k). This result implies a polynomial lower bound on PARALLEL TIME · HARDWARE of parallel RAM's.Lower bounds on the complexity measures TIME · SPACE and REVERSALS · SPACE of nondeterministic machines are direct consequences of the result introduced above.All lower bounds obtained are substantially improved in the case that SPACE⩾ nɛ for 0<ɛ<1. Several strongest lower bounds for two-way and one-way alternating (deterministic, nondeterministic) multihead finite automata are obtained as direct consequences of these results. The hierarchies for the complexity measures TSP, RSP, TS and RS can be immediately achieved too
Automata with Modulo Counters and Nondeterministic Counter Bounds
We introduce and investigate Nondeterministically Bounded Modulo Counter
Automata (NBMCA), which are two-way multi-head automata that comprise a
constant number of modulo counters, where the counter bounds are nondeterministically
guessed, and this is the only element of nondeterminism. NBMCA are
tailored to recognising those languages that are characterised by the existence of
a specific factorisation of their words, e. g., pattern languages. In this work, we
subject NBMCA to a theoretically sound analysis
On space-bounded synchronized alternating Turing machines
AbstractWe continue the study of the computational power of synchronized alternating Turing machines (SATM) introduced in (Hromkovič 1986, Slobodová 1987, 1988a, b) to allow communication via synchronization among processes of alternating Turing machines. We are interested in comparing the four main classes of space-bounded synchronized alternating Turing machines obtained by adding or removing off-line capability and nondeterminism (1SUTM(S(n)), SUTM(S(n)), 1SATM(S(n)), and SATM(S(n)) against one another and against other variants of alternating Turing machines. Denoting the class of languages accepted by machines in C by L(C), we show as our main results that L(1SUTM(S(n))) ⊂ L(SUTM(S(n))) ⊂ L(1SATM(S(n)))= L(SATM(S(n))) for all space-bounded functions S(n)ϵo(n), and L(1SUTM(S(n)))= L(SUTM(S(n))) ⊂ L(1SATM(S(n)))=L(SATM(S(n))) for S(n)) ⩾ n. Furthermore, we show that for log log(n) ⩽ S(n)ϵo(log(n)), L(1SUTM(S(n))) is incomparable to L[1] ATM(S(n))). L(UTM(S(n))), L(1MUTM(S(n))), and L(MUTM(S(n))), where MATMs are alternating Turing machines with modified acceptance proposed in (Inoue 1989); in contrast, we show that these relationships become proper inclusions when log(n) ⩽ S(n)ϵo(n).For deterministic synchronized alternating finite automata with at most k processes (1DSA(k)FA and DSA(k)FA) we establish a tight hierarchy on the number of processes for the one-way case, namely, L(1DSA(n)FA) ⊂ L(1DSA(n+1)FA) for all n > 0, and show that L(1DFA(2)) − ∪k=1∞L(DSA(k)FA) ≠ ∅, where DFA(k) denotes deterministic k-head finite automata. Finally we investigate closure properties under Boolean operations for some of these classes of languages
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