Hirsch, R. (1997). Expressive power and complexity in algebraic logic. Journal of Logic and Computation, 7(3):309--351. Home/Search Document Details and Download
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Reasoning About Temporal Constraints: Classifying The.. - Krokhin, Jeavons (Correct)
....as most similar results) was achieved by computerassisted exhaustive search. However, it was noted in [9] that, for further progress, theoretical studies of the structure of Allen s algebra are required. There are some theoretical investigations of the structure of Allen s algebra, see, e.g. [12, 13, 16]) However they generally allow more operations on relations than originally used in [1] which makes them inappropriate for classifying complexity within the interval algebra. In this paper we systematically use algebraic method that is similar to the approach taken in [18] The rst novel ....
Robin Hirsch. Expressive power and complexity in algebraic logic. Journal of Logic and Computation, 7(3):309-351, 1997.
Reasoning About Temporal Relations: The Tractable.. - Krokhin, Jeavons (2001) (1 citation) (Correct)
....Allen s algebra are necessary, since using the method from that paper for a complete analysis of complexity would require dealing with more than 10 50 individual cases, which is clearly not feasible. There have been some theoretical investigations of the structure of Allen s algebra, see, e.g. [24, 25, 34]) however they consider relation algebras in the sense de ned by Tarski [51] that is, they generally allow more operations on relations than originally used in [1] which makes them inappropriate for classifying complexity within the interval algebra. In fact, none of the maximal tractable ....
R. Hirsch. Expressive power and complexity in algebraic logic. Journal of Logic and Computation, 7(3):309-351, 1997. 51
A Relation-Algebraic Approach to the Region Connection.. - Düntsch, Wang, McCloskey (Correct)
....Galois closed if and only if B is homogeneous. Another area which deserves to be looked at is the complexity of mereological RAs. The complexity of Allen s interval algebra has been studied by Ladkin and Maddux (1994) and more general results, which may serve as a starting point, can be found in Hirsch (1997). 6 Acknowledgements We should like to thank H. Andrka, B. Bennett, C. Eschenbach, I. Nmeti, J. Stell and M. Worboys for fruitful discussions on the subject and helpful remarks. ....
Hirsch, R. (1997). Expressive power and complexity in algebraic logic. Journal of Logic and Computation, 7(3), 309--351.
The Complexity of Constraint Satisfaction Problems For Small.. - Hirsch Self-citation (Hirsch) (Correct)
....e.g. the Allen Interval Algebra, this consistency checking problem was shown to be NP complete [21, theorems 2 and 3] An investigation, very relevant to the work conducted here, is in [29] where some small algebras are studied . Further complexity analysis of various algebras can be found in [31]. Typically, it seems, the complexity of the constraint satisfaction problem for many relation algebras is NP hard. For some pathological, finite relation algebras the problem can even be undecidable [32] A systematic analysis of the complexity of the constraint handling for finite relation ....
....are not essentially different . The disadvantage of the restriction to square representations is that non simple relation algebras do not possess square representations, and so, following [30] we do not define the spectrum of a non simple relation algebra. as the satisfiability of a network [31]. DEFINITION 2 (1) Given a Relation Algebra A and a set of variable names X = fx 0 ; x 1 ; x n ; g, the logical expression ax i x j , where a is an element of A, and x i and x j are elements of X , is called a constraint over A. 2) Given a representation M of A, a variable ....
R. Hirsch, Expressive power and complexity in algebraic logic, Journal of Logic and Computation 7 (3) (1997) 309--351.
Tractable Approximations for Temporal Constraint Handling - Hirsch (1999) (2 citations) Self-citation (Hirsch) (Correct)
....in a flow of time that branches into the future [Com83] the metric point algebra [DMP91] which includes metric constraints on the distance between points (though this algebra is infinite) the containment algebra [LM94] which is a subalgebra of the Allen interval algebra and many others. See [Hir97] for more about these algebras and their complexities. It is typically the case that the NSP is NP hard, though the point algebra and the left linear algebras are exceptions. The point of this paper is to provide a series of tractable algorithms which approximate satisfiability checking for the ....
R Hirsch. Expressive power and complexity in algebraic logic. Journal of Logic and Computation, 7(3):309--351, 1997.
Relation Algebras and Their Application in Qualitative Spatial.. - Düntsch (2003) (Correct)
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Hirsch, R. (1997). Expressive power and complexity in algebraic logic. Journal of Logic and Computation, 7(3):309--351.
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