Unambiguity of circuits

Lange, Klaus-Jörn

doi:10.1109/sct.1990.113962

Cited by 8 publications

(20 citation statements)

References 11 publications

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“…In Section 3 we show the inclusion of UnambSAC k in UnambAPDA k using an inductive counting technique. This surprising relationship answers an open question of [Lan90], where this inclusion was conjectured to be wrong or at least very hard to obtain. Furthermore, we show UnambSAC k to be closed under complementation.…”

Section: Introductionmentioning

confidence: 57%

“…Further evidence of relationship between CREW-PRAMs and unambiguous complexity classes followed from a circuit characterization of CREW-PRAMs. Analogously to CRCW k = AC k (see [SV85]), a similar equation CREW k = UnambAC k was proved in [Lan90]. For this purpose, semi-unbounded, unambiguous circuits had to be dened.…”

Section: Introductionmentioning

confidence: 92%

“…In contrast to UnambSAC k , in UnambRAC k circuits also OR-gates of bounded fan-in have to be vulnerable. In [Lan90] We suppose all circuit families to be U BC -uniform, that is, a description of the nth circuit can be computed by some z(n) space bounded Turing machine, where z(n) is the size of the circuit (cf.…”

Section: Introductionmentioning

confidence: 99%

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Unambiguous simulations of auxiliary pushdown automata and circuits

Niedermeier

Rossmanith

1992

Latin '92

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In this paper time-bounded auxiliary push-down automata (AuxPDA), i.e. time and space bounded Turing machines with additional pushdown store, are considered. We investigate the power of unambiguous AuxPDA, i.e., machines that have at most one accepting computation, and ambiguity bounded AuxPDA.Recently, it was shown by Buntrock, Hemachandra, and Siefkes that space bounded Turing machines, whose computation trees have moderate ambiguity, can be eciently simulated by unambiguous AuxPDA with same space bound. This paper shows that such an ecient simulation is also possible for AuxPDA. The simulation incorporates no space and time penalty, unless the ambiguity is very high.By similar methods it is shown that unambiguous AuxPDA can eciently simulate a certain class of unambiguous, semi-unbounded fan-in circuits, which answers an open question posed by Lange.Finally, obliviousness for AuxPDA is considered and it is proved that unambiguous Aux-PDA work w.l.o.g. with a very limited amount of space on the pushdown store, a result that is already known for deterministic and nondeterministic AuxPDA.

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Section: Introductionmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 92%

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Unambiguous simulations of auxiliary pushdown automata and circuits

Niedermeier

Rossmanith

1992

Latin '92

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“…Exclusive write PRAMs are intermediate in computational power between owner write and concurrent write PRAMS and the same holds for read access. While the owner and the concurrent concept are closely related to determinism and nondeterminism [24,42,59], the concept of exclusiveness corresponds to unambiguity [41,42,48], which explains the inconstructive features of this concept. Correspondingly, we get two ways to manage read access: Concurrent Read and Owner Read.…”

Section: Parallel Random Access Machinesmentioning

confidence: 99%

Data Independence of Read, Write, and Control Structures in PRAM Computations

Lange

Niedermeier

2000

Journal of Computer and System Sciences

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We introduce the notions of control and communication structures in PRAM computations and relate them to the concept of data independence. Our main result is to characterize differences between unbounded fan-in parallelism AC k , bounded fan-in parallelism NC k , and the sequential classes DSPACE(log n) and LOGDCFL in terms of a PRAM's communication structure and instruction set. Our findings give a concrete indication that in parallel computations writing is more powerful than reading. Further characterizations are given for parallel pointer machines and the semiunbounded fan-in circuit classes SAC k

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“…It is known that NC 1 circuits can be made unambiguous [Lan93]. In terms of arithmetic circuits, this yields:…”

Section: Introductionmentioning

confidence: 99%

Counting Classes and the Fine Structure between NC 1 and L

Datta

Mahajan

Rao

et al. 2010

Mathematical Foundations of Computer Science 2010

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The class NC 1 of problems solvable by bounded fan-in circuit families of logarithmic depth is known to be contained in logarithmic space L, but not much about the converse is known. In this paper we examine the structure of classes in between NC 1 and L based on counting functions or, equivalently, based on arithmetic circuits. The classes PNC 1 and C = NC 1 , defined by a test for positivity and a test for zero, respectively, of arithmetic circuit families of logarithmic depth, sit in this complexity interval. We study the landscape of Boolean hierarchies, constant-depth oracle hierarchies, and logarithmic-depth oracle hierarchies over PNC 1 and C = NC 1 . We provide complete problems, obtain the upper bound L for all these hierarchies, and prove partial hierarchy collapses. In particular, the constant-depth oracle hierarchy over PNC 1 collapses to its first level PNC 1 , and the constant-depth oracle hierarchy over C = NC 1 collapses to its second level.

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Unambiguity of circuits

Abstract: The concept of unambiguity of circuits is considered. Several classes of unambiguous circuitfamilies within the NC-hierarchy are introduced and related to unambiguous automata and to PRAM's with exclusive writeaccess. In particular, we show CREW-TIME(logn) = Unum bA C1.

Cited by 8 publications

References 11 publications

Unambiguous simulations of auxiliary pushdown automata and circuits

Unambiguous simulations of auxiliary pushdown automata and circuits

Data Independence of Read, Write, and Control Structures in PRAM Computations

Counting Classes and the Fine Structure between NC 1 and L

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