Reversal-bounded computations:
IN computations by abstract computing devices such as the Turing machine, head reversals are required for searching the input or retrieving intermediate results. Hence the number of head reversals is a measure of the complexity of a computation. This thesis is a study of reversal-bounded computation...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Mikrofilm Buch |
| Sprache: | English |
| Veröffentlicht: |
1980
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| Ausgabe: | [Mikrofiche-Ausg.] |
| Schlagworte: | |
| Zusammenfassung: | IN computations by abstract computing devices such as the Turing machine, head reversals are required for searching the input or retrieving intermediate results. Hence the number of head reversals is a measure of the complexity of a computation. This thesis is a study of reversal-bounded computation on three models of abstract computing devices The first model is the 1-tape Turing machine with finite bounds on head reversals. It is known that such machines recognize exactly the regular sets so that for recognition purposes, reversals can be eliminated entirely. For transduction purposes, that is, if an output is expected on the tape, a single reversal suffices. Hence these machines are most appropriately called finite automata. Clearly they are among the weakest possible computing devices, and many decision problems about them are solvable. We use this fact and a very simple input-output encoding scheme to obtain greatly simplified proofs of the decidability of some weak mathematical theories, including the weak monadic second-order theory of one successor and Presburger arithmetic. Similar techniques yield linear size bounds as well as linear time complexity bounds (on the multitape Turing machine model) for functions definable in Presburger arithmetic. As corollaries, we find applications in linear diophantine systems and linear integer programming Lastly, we consider finite reversal-bounded multitape finite automata. We show that over a single-letter alphabet, the languages accepted are exactly the unary encodings of Presburger relations. This result holds whether the model is deterministic or nondeterministic, and even if it is augmented with, for example, finite reversal-bounded counters and an unrestricted pushdown store, or if the reversals are restricted to rewinds, that is, instructions that simultaneously position all heads at the beginnings of their respective tapes. For both deterministic and nondeterministic rewind automata, we establish exhaustive hierarchies based on the finite number of rewinds. When restricted to a single-letter alphabet, the deterministic hierarchy stands but the nondeterministic one collapses |
| Beschreibung: | VI, 156 S. graph. Darst. |
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| 502 | |a Ithaca, NY, Univ., Diss., 1980 | ||
| 520 | 3 | |a IN computations by abstract computing devices such as the Turing machine, head reversals are required for searching the input or retrieving intermediate results. Hence the number of head reversals is a measure of the complexity of a computation. This thesis is a study of reversal-bounded computation on three models of abstract computing devices | |
| 520 | 3 | |a The first model is the 1-tape Turing machine with finite bounds on head reversals. It is known that such machines recognize exactly the regular sets so that for recognition purposes, reversals can be eliminated entirely. For transduction purposes, that is, if an output is expected on the tape, a single reversal suffices. Hence these machines are most appropriately called finite automata. Clearly they are among the weakest possible computing devices, and many decision problems about them are solvable. We use this fact and a very simple input-output encoding scheme to obtain greatly simplified proofs of the decidability of some weak mathematical theories, including the weak monadic second-order theory of one successor and Presburger arithmetic. Similar techniques yield linear size bounds as well as linear time complexity bounds (on the multitape Turing machine model) for functions definable in Presburger arithmetic. As corollaries, we find applications in linear diophantine systems and linear integer programming | |
| 520 | 3 | |a Lastly, we consider finite reversal-bounded multitape finite automata. We show that over a single-letter alphabet, the languages accepted are exactly the unary encodings of Presburger relations. This result holds whether the model is deterministic or nondeterministic, and even if it is augmented with, for example, finite reversal-bounded counters and an unrestricted pushdown store, or if the reversals are restricted to rewinds, that is, instructions that simultaneously position all heads at the beginnings of their respective tapes. For both deterministic and nondeterministic rewind automata, we establish exhaustive hierarchies based on the finite number of rewinds. When restricted to a single-letter alphabet, the deterministic hierarchy stands but the nondeterministic one collapses | |
| 533 | |a Mikroform-Ausgabe |b Ann Arbor, Mich. |c Univ. Microfilms Internat. |d 1981 |e 2 Mikrofiches |n Mikrofiche-Ausg.: |7 s1981 | ||
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| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 776 | 0 | 8 | |i Reproduktion von |a Chan, Tat-Hung |t Reversal-bounded computations |d 1980 |
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| author | Chan, Tat-Hung |
| author_facet | Chan, Tat-Hung |
| author_role | aut |
| author_sort | Chan, Tat-Hung |
| author_variant | t h c thc |
| building | Verbundindex |
| bvnumber | BV037488697 |
| ctrlnum | (OCoLC)734088747 (DE-599)BVBBV037488697 |
| dewey-full | 510.782 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
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| dewey-search | 510.782 |
| dewey-sort | 3510.782 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | [Mikrofiche-Ausg.] |
| format | Thesis Microfilm Book |
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| indexdate | 2024-07-09T23:25:15Z |
| institution | BVB |
| language | English |
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| physical | VI, 156 S. graph. Darst. |
| publishDate | 1980 |
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| spelling | Chan, Tat-Hung Verfasser aut Reversal-bounded computations Tat-Hung Chan [Mikrofiche-Ausg.] 1980 VI, 156 S. graph. Darst. txt rdacontent h rdamedia he rdacarrier Ithaca, NY, Univ., Diss., 1980 IN computations by abstract computing devices such as the Turing machine, head reversals are required for searching the input or retrieving intermediate results. Hence the number of head reversals is a measure of the complexity of a computation. This thesis is a study of reversal-bounded computation on three models of abstract computing devices The first model is the 1-tape Turing machine with finite bounds on head reversals. It is known that such machines recognize exactly the regular sets so that for recognition purposes, reversals can be eliminated entirely. For transduction purposes, that is, if an output is expected on the tape, a single reversal suffices. Hence these machines are most appropriately called finite automata. Clearly they are among the weakest possible computing devices, and many decision problems about them are solvable. We use this fact and a very simple input-output encoding scheme to obtain greatly simplified proofs of the decidability of some weak mathematical theories, including the weak monadic second-order theory of one successor and Presburger arithmetic. Similar techniques yield linear size bounds as well as linear time complexity bounds (on the multitape Turing machine model) for functions definable in Presburger arithmetic. As corollaries, we find applications in linear diophantine systems and linear integer programming Lastly, we consider finite reversal-bounded multitape finite automata. We show that over a single-letter alphabet, the languages accepted are exactly the unary encodings of Presburger relations. This result holds whether the model is deterministic or nondeterministic, and even if it is augmented with, for example, finite reversal-bounded counters and an unrestricted pushdown store, or if the reversals are restricted to rewinds, that is, instructions that simultaneously position all heads at the beginnings of their respective tapes. For both deterministic and nondeterministic rewind automata, we establish exhaustive hierarchies based on the finite number of rewinds. When restricted to a single-letter alphabet, the deterministic hierarchy stands but the nondeterministic one collapses Mikroform-Ausgabe Ann Arbor, Mich. Univ. Microfilms Internat. 1981 2 Mikrofiches Mikrofiche-Ausg.: s1981 Computational complexity Turing machines (DE-588)4113937-9 Hochschulschrift gnd-content Reproduktion von Chan, Tat-Hung Reversal-bounded computations 1980 |
| spellingShingle | Chan, Tat-Hung Reversal-bounded computations Computational complexity Turing machines |
| subject_GND | (DE-588)4113937-9 |
| title | Reversal-bounded computations |
| title_auth | Reversal-bounded computations |
| title_exact_search | Reversal-bounded computations |
| title_full | Reversal-bounded computations Tat-Hung Chan |
| title_fullStr | Reversal-bounded computations Tat-Hung Chan |
| title_full_unstemmed | Reversal-bounded computations Tat-Hung Chan |
| title_short | Reversal-bounded computations |
| title_sort | reversal bounded computations |
| topic | Computational complexity Turing machines |
| topic_facet | Computational complexity Turing machines Hochschulschrift |
| work_keys_str_mv | AT chantathung reversalboundedcomputations |