Complexity and uniformity of elimination in Presburger arithmetic:
Abstract: "The decision complexity of Presburger Arithmetic PA and its variants has received much attention in the literature. We investigate the complexity of quantifier elimination procedures for PA -- a topic that is even more relevant for applications. First we show that the the [sic] autho...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Passau
1997
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| Series: | MIP / Universität Passau, Fakultät für Mathematik und Informatik
1997,03 |
| Subjects: | |
| Summary: | Abstract: "The decision complexity of Presburger Arithmetic PA and its variants has received much attention in the literature. We investigate the complexity of quantifier elimination procedures for PA -- a topic that is even more relevant for applications. First we show that the the [sic] author's triply exponential upper bound is essentially tight. This fact seems to preclude practical applications. By weakening the concept of quantifier elimination slightly to bounded quantifier elimination, we show, however, that the upper and lower bound for quantifier elimination in PA can be lowered by exactly one exponential. Moreover we gain uniformity in the coefficients, a property that we prove to be impossible for complete quantifier elimination in PA. Thus we have tight upper and lower complexity bounds for elimination theory in PA and uniform PA. The results are inspired by experimental implementations of bounded quantifier elimination that have solved non-trivial application problems e.g. in parametric integer programming." |
| Physical Description: | 13, 5 S. |
Staff View
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| id | DE-604.BV011221929 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-10T17:04:59Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007529238 |
| oclc_num | 38179100 |
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| physical | 13, 5 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
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| series2 | MIP / Universität Passau, Fakultät für Mathematik und Informatik |
| spelling | Weispfenning, Volker 1944- Verfasser (DE-588)108063550 aut Complexity and uniformity of elimination in Presburger arithmetic Volker Weispfenning Passau 1997 13, 5 S. txt rdacontent n rdamedia nc rdacarrier MIP / Universität Passau, Fakultät für Mathematik und Informatik 1997,03 Abstract: "The decision complexity of Presburger Arithmetic PA and its variants has received much attention in the literature. We investigate the complexity of quantifier elimination procedures for PA -- a topic that is even more relevant for applications. First we show that the the [sic] author's triply exponential upper bound is essentially tight. This fact seems to preclude practical applications. By weakening the concept of quantifier elimination slightly to bounded quantifier elimination, we show, however, that the upper and lower bound for quantifier elimination in PA can be lowered by exactly one exponential. Moreover we gain uniformity in the coefficients, a property that we prove to be impossible for complete quantifier elimination in PA. Thus we have tight upper and lower complexity bounds for elimination theory in PA and uniform PA. The results are inspired by experimental implementations of bounded quantifier elimination that have solved non-trivial application problems e.g. in parametric integer programming." REDUCE Computational complexity Computer arithmetic Integer programming Theoretische Informatik (DE-588)4196735-5 gnd rswk-swf Informatik (DE-588)4026894-9 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Theoretische Informatik (DE-588)4196735-5 s Informatik (DE-588)4026894-9 s Mathematik (DE-588)4037944-9 s DE-604 Universität Passau, Fakultät für Mathematik und Informatik MIP 1997,03 (DE-604)BV000905393 1997,03 |
| spellingShingle | Weispfenning, Volker 1944- Complexity and uniformity of elimination in Presburger arithmetic REDUCE Computational complexity Computer arithmetic Integer programming Theoretische Informatik (DE-588)4196735-5 gnd Informatik (DE-588)4026894-9 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4196735-5 (DE-588)4026894-9 (DE-588)4037944-9 |
| title | Complexity and uniformity of elimination in Presburger arithmetic |
| title_auth | Complexity and uniformity of elimination in Presburger arithmetic |
| title_exact_search | Complexity and uniformity of elimination in Presburger arithmetic |
| title_full | Complexity and uniformity of elimination in Presburger arithmetic Volker Weispfenning |
| title_fullStr | Complexity and uniformity of elimination in Presburger arithmetic Volker Weispfenning |
| title_full_unstemmed | Complexity and uniformity of elimination in Presburger arithmetic Volker Weispfenning |
| title_short | Complexity and uniformity of elimination in Presburger arithmetic |
| title_sort | complexity and uniformity of elimination in presburger arithmetic |
| topic | REDUCE Computational complexity Computer arithmetic Integer programming Theoretische Informatik (DE-588)4196735-5 gnd Informatik (DE-588)4026894-9 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | REDUCE Computational complexity Computer arithmetic Integer programming Theoretische Informatik Informatik Mathematik |
| volume_link | (DE-604)BV000905393 |
| work_keys_str_mv | AT weispfenningvolker complexityanduniformityofeliminationinpresburgerarithmetic |