Does indirect addressing matter?

Brand, Michael

doi:10.1007/s00236-012-0171-1

Cited by 4 publications

(5 citation statements)

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“…This last mode, which can also be used to define the target register, is known as "indirect addressing". In [3] it is proved that for the RAMs considered here indirect addressing has no effect. We therefore assume throughout that it is unavailable to the RAMs.…”

Section: Introductionmentioning

confidence: 84%

“…The result will be that the new head value is 0. 3 To avoid this, we introduce a new element into the simulation. This is a constant.…”

Section: Lemma 5 a Tm Can Be Simulated By A Ram[← → Bool] Using Only ...mentioning

confidence: 99%

“…We allow this simulation to use a larger set of tape symbols than the original {0, 1}, knowing that this costs at most a linear increase in the amount of space required [15], which cannot violate the EL op (O(f (n)) bound. Furthermore, as per [3], we continue to consider only RAMs that make no use of indirect addressing (and are therefore known to only access a finite number of registers).…”

Section: Lemma 8 For Op = {← → [+] [ ] Bool} If a Ram[op] Does Not Us...mentioning

confidence: 99%

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Computing with and without Arbitrary Large Numbers

Brand

2013

Lecture Notes in Computer Science

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In the study of random access machines (RAMs) it has been shown that the availability of an extra input integer, having no special properties other than being sufficiently large, is enough to reduce the computational complexity of some problems. However, this has only been shown so far for specific problems. We provide a characterization of the power of such extra inputs for general problems.To do so, we first correct a classical result by Simon and Szegedy (1992) as well as one by Simon (1981). In the former we show mistakes in the proof and correct these by an entirely new construction, with no great change to the results. In the latter, the original proof direction stands with only minor modifications, but the new results are far stronger than those of Simon (1981).In both cases, the new constructions provide the theoretical tools required to characterize the power of arbitrary large numbers.1 Arithmetic complexity is the computational complexity of a problem under the RAM[+, , ×, ÷] model, which is defined later on in this section.

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Section: Introductionmentioning

confidence: 84%

“…The result will be that the new head value is 0. 3 To avoid this, we introduce a new element into the simulation. This is a constant.…”

Section: Lemma 5 a Tm Can Be Simulated By A Ram[← → Bool] Using Only ...mentioning

confidence: 99%

Section: Lemma 8 For Op = {← → [+] [ ] Bool} If a Ram[op] Does Not Us...mentioning

confidence: 99%

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Computing with and without Arbitrary Large Numbers

Brand

2013

Lecture Notes in Computer Science

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“…To do this, we initialise R ′ [k + 1] to be 1, and proceed with the simulation by translating any action by the simulated RAM on R[i], for any i, to the same action on R ′ [i]. 4 We do this for all actions except R[i] → X, which is an operation that is unavailable to the simulating RAM.…”

Section: Some Redundant Operationsmentioning

confidence: 99%

“…Consider the following definitions, following [4]: Definition 2 (Vectors). A triplet (m, V, n) of integers will be called an encoded vector.…”

Section: Vectors and Tableauxmentioning

confidence: 99%

The RAM equivalent of P vs. RP

Brand

2013

Preprint

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One of the fundamental open questions in computational complexity is whether the class of problems solvable by use of stochasticity under the Random Polynomial time (RP) model is larger than the class of those solvable in deterministic polynomial time (P). However, this question is only open for Turing Machines, not for Random Access Machines (RAMs).Simon ( 1981) was able to show that for a sufficiently equipped Random Access Machine, the ability to switch states nondeterministically does not entail any computational advantage. However, in the same paper, Simon describes a different (and arguably more natural) scenario for stochasticity under the RAM model. According to Simon's proposal, instead of receiving a new random bit at each execution step, the RAM program is able to execute the pseudofunction RAND(y), which returns a uniformly distributed random integer in the range [0, y). Whether the ability to allot a random integer in this fashion is more powerful than the ability to allot a random bit remained an open question for the last 30 years.In this paper, we close Simon's open problem, by fully characterising the class of languages recognisable in polynomial time by each of the RAMs regarding which the question was posed. We show that for some of these, stochasticity entails no advantage, but, more interestingly, we show that for others it does.

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Constant-time sorting

Brand

2014

Information and Computation

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Does indirect addressing matter?

Cited by 4 publications

References 5 publications

Computing with and without Arbitrary Large Numbers

Computing with and without Arbitrary Large Numbers

The RAM equivalent of P vs. RP

Constant-time sorting

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