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: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Ithaca, NY
1980
|
| Schriftenreihe: | Cornell University <Ithaca, NY> / Department of Computer Science: Technical report
448 |
| 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: | Zugl.: Ithaca, NY, Cornell Univ., Diss. |
| Beschreibung: | 156 Sp. graph. Darst. |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV010010564 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 950127s1980 d||| m||| 00||| engod | ||
| 035 | |a (OCoLC)7962431 | ||
| 035 | |a (DE-599)BVBBV010010564 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G | ||
| 082 | 0 | |a 510.782 |b C45r | |
| 100 | 1 | |a Chan, Tat-Hung |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Reversal-bounded computations |c Tat-hung Chan |
| 264 | 1 | |a Ithaca, NY |c 1980 | |
| 300 | |a 156 Sp. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cornell University <Ithaca, NY> / Department of Computer Science: Technical report |v 448 | |
| 500 | |a Zugl.: Ithaca, NY, Cornell Univ., Diss. | ||
| 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 | |
| 650 | 4 | |a Computational complexity | |
| 650 | 4 | |a Turing machines | |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 810 | 2 | |a Department of Computer Science: Technical report |t Cornell University <Ithaca, NY> |v 448 |w (DE-604)BV006185504 |9 448 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006637469 | ||
Datensatz im Suchindex
| _version_ | 1804124390076448768 |
|---|---|
| any_adam_object | |
| 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 | BV010010564 |
| ctrlnum | (OCoLC)7962431 (DE-599)BVBBV010010564 |
| dewey-full | 510.782 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.782 |
| dewey-search | 510.782 |
| dewey-sort | 3510.782 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03309nam a2200361 cb4500</leader><controlfield tag="001">BV010010564</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">950127s1980 d||| m||| 00||| engod</controlfield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)7962431</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010010564</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510.782</subfield><subfield code="b">C45r</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Chan, Tat-Hung</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Reversal-bounded computations</subfield><subfield code="c">Tat-hung Chan</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Ithaca, NY</subfield><subfield code="c">1980</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">156 Sp.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Cornell University <Ithaca, NY> / Department of Computer Science: Technical report</subfield><subfield code="v">448</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Zugl.: Ithaca, NY, Cornell Univ., Diss.</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="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</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="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</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="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</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computational complexity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Turing machines</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4113937-9</subfield><subfield code="a">Hochschulschrift</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="810" ind1="2" ind2=" "><subfield code="a">Department of Computer Science: Technical report</subfield><subfield code="t">Cornell University <Ithaca, NY></subfield><subfield code="v">448</subfield><subfield code="w">(DE-604)BV006185504</subfield><subfield code="9">448</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-006637469</subfield></datafield></record></collection> |
| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV010010564 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:44:54Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006637469 |
| oclc_num | 7962431 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | 156 Sp. graph. Darst. |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| record_format | marc |
| series2 | Cornell University <Ithaca, NY> / Department of Computer Science: Technical report |
| spelling | Chan, Tat-Hung Verfasser aut Reversal-bounded computations Tat-hung Chan Ithaca, NY 1980 156 Sp. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cornell University <Ithaca, NY> / Department of Computer Science: Technical report 448 Zugl.: Ithaca, NY, Cornell Univ., Diss. 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 Computational complexity Turing machines (DE-588)4113937-9 Hochschulschrift gnd-content Department of Computer Science: Technical report Cornell University <Ithaca, NY> 448 (DE-604)BV006185504 448 |
| 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 |
| volume_link | (DE-604)BV006185504 |
| work_keys_str_mv | AT chantathung reversalboundedcomputations |