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Loui, Michael C. Luginbuhl, David Ralph 2011-05-07T13:50:41Z 2011-05-07T13:50:41Z 10000-01-01 1990 The relative power of several computational models is considered. These models are the Turing machine and its multidimensional variant, the random access machine (RAM), the tree machine, and the pointer machine. The basic computational properties of the pointer machine are examined in more detail. For example, time and space hierarchy theorems for pointer machines are presented. Every Turing machine of time complexity $t$ and space complexity $s$ can be simulated by a pointer machine of time complexity $O$($t$) using $O$($s$/log $s$) nodes. This strengthens a similar result by van Emde Boas (1989). Every alternating pointer machine of time complexity $t$ can be simulated by a deterministic pointer machine using $O$($t$/log $t$) nodes. Other results concerning nondeterministic and alternating pointer machines are presented. Every tree machine of time complexity $t$ can be simulated on-line by a log-cost RAM of time complexity $O$(($t$log $t$)/log log $t$). This simulation is shown to be optimal using the notion of incompressibility from Kolmogorov complexity (Solomonoff, 1964; Kolmogorov, 1965). Every $d$-dimensional Turing machine of time complexity $t$ can be simulated on-line by a log-cost RAM running in time $O$($t$(log $t$)$\sp{1-(1/d)}$)(log log $t$)$\sp{(1/d}$). There is a log-cost RAM $R$ running in time $t$ such that every $d$-dimensional Turing machine requires time $\Omega$($t\sp{1+(1/d)}$/(log $t$(log log $t$)$\sp{1+(1/d)}$)) to simulate $R$ on-line. Every unit-cost RAM of time complexity $t$ can be simulated on-line by a $d$-dimensional Turing machine in time $O$($t$($n$)$\sp2$log $t$($n$)). Made available in DSpace on 2011-05-07T13:50:41Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9026259.pdf: 3294983 bytes, checksum: 09e2fa4d15fc66aa6b9f836a03bc9fc8 (MD5) Previous issue date: 1990 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:59:50Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:28:16-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only AAI9026259 (UMI)AAI9026259 http://hdl.handle.net/2142/22763 eng Copyright 1990 Luginbuhl, David Ralph Mathematics Computer Science Computational complexity of random-access models text Computer Science Computer Science University of Illinois at Urbana-Champaign Dissertation Ph.D.