A. Livchak, The relational model for process control, Automated Documentation and Mathematical Linguistics, vol. 4 (1983), pp. 27--29. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Finite Variable Logics In Descriptive Complexity Theory - Grohe (1998) (4 citations) (Correct)
....C. As I have mentioned, the class O of ordered structures plays a central role. As a matter of fact, in the literature capturing is often only defined for ordered structures. For us, the most important capturing result on ordered structures is the following: Theorem 8. 5 (Immerman [46] Livchak [56], Vardi [70] IFP captures PTIME on the class of ordered structures. Other well known results, due to Immerman [48] are that deterministic transitive closure logic captures LOGSPACE and transitive closure logic captures NLOGSPACE on ordered structures. The reason for the importance of an order ....
A. Livchak. The relational model for process control. Automated Documentation and Mathematical Linguistics, 4:27--29, 1983.
Fixed-Point Logics on Planar Graphs - Grohe (1998) (7 citations) (Correct)
....be extended to arbitrary structures, but this is no longer the case for the classes below. In particular, inflationary fixed point logic IFP captures P on the class of ordered structures (this result, henceforth referred to as the ILV Theorem, has independently proved by Immerman [6] Livchak [10], and Vardi [15] but not on arbitrary structures. The question of whether there exists a reasonable logic that captures P on arbitrary structures remains one of the most challenging in finite model theory. Some partial results are known besides the ILV Theorem. In particular, Immerman and ....
....X A 0 = and X A i 1 = X A i [ fa 2 A j A j= a; X A i )g. We let X A 1 = S i0 X A i . Then A j= IFP x;X ]t ( t A 2 X A 1 ; where t A denotes the interpretation of the term tuple t in A. The following ILV Theorem has independently been proved by Immerman [5] Livchak [10], and Vardi [15] in slightly different formulations. The version of the result we state here goes back to Gurevich [3] Theorem 2.2 IFP captures P on the class of ordered structures. Our results are based on the following corollary. Let D be a class of structures and (x; y; z 1 ; z k ....
A. Livchak. The relational model for process control. Automated Documentation and Mathematical Linguistics, 4:27-- 29, 1983.
Finite Variable Logics In Descriptive Complexity Theory - Grohe (1998) (4 citations) Self-citation (Model) (Correct)
....C. As I have mentioned, the class O of ordered structures plays a central role. As a matter of fact, in the literature capturing is often only defined for ordered structures. For us, the most important capturing result on ordered structures is the following: Theorem 8. 5 (Immerman [46] Livchak [56], Vardi [70] IFP captures PTIME on the class of ordered structures. Other well known results, due to Immerman [48] are that deterministic transitive closure logic captures LOGSPACE and transitive closure logic captures NLOGSPACE on ordered structures. The reason for the importance of an order ....
A. Livchak, The relational model for process control, Automated Documentation and Mathematical Linguistics, vol. 4 (1983), pp. 27--29.
Finite Variable Logics In Descriptive Complexity Theory - Grohe (1998) (4 citations) Self-citation (Model) (Correct)
....C. As I have mentioned, the class O of ordered structures plays a central role. As a matter of fact, in the literature capturing is often only defined for ordered structures. For us, the most important capturing result on ordered structures is the following: Theorem 8. 5 (Immerman [46] Livchak [56], Vardi [70] IFP captures PTIME on the class of ordered structures. Other well known results, due to Immerman [48] are that deterministic transitive closure logic captures LOGSPACE and transitive closure logic captures NLOGSPACE on ordered structures. The reason for the importance of an ....
A. Livchak. The relational model for process control. Automated Documentation and Mathematical Linguistics, 4:27--29, 1983.
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