Complexity of deciding Tarski algebra
Let a formula of Tarski algebra contain k atomic subformulas of the kind ( f i ⩾ 0), 1 ⩽ t ⩽ k, where the polynomials f i ∈ ℤ [ X 1,..., X n ] have degrees deg ( f i ) < d, let 2 M be an upper bound for the absolute value of every coeffieient of the polynomials f i , 1 ⩽ i ⩽ k, let a ⩽ n be the n...
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| Published in | Journal of symbolic computation Vol. 5; no. 1; pp. 65 - 108 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
1988
Elsevier |
| Subjects | |
| Online Access | Get full text |
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| Summary: | Let a formula of Tarski algebra contain
k atomic subformulas of the kind (
f
i
⩾ 0), 1 ⩽
t ⩽
k, where the polynomials
f
i
∈ ℤ [
X
1,...,
X
n
] have degrees deg (
f
i
) <
d, let 2
M
be an upper bound for the absolute value of every coeffieient of the polynomials
f
i
, 1 ⩽
i ⩽
k, let
a ⩽
n be the number of quantifier alternations in the prenex form of the formula. A decision method for Tarski algebra is described with the running time polynomial in
M
(
k
d
)
(
O
(
n
)
)
4
n
−
2
. Previously known decision procedures have a time complexity polynomial in
(
M
k
d
)
2
O
(
n
)
. |
|---|---|
| ISSN: | 0747-7171 1095-855X |
| DOI: | 10.1016/S0747-7171(88)80006-3 |