Languages that capture complexity classes
SIAM Journal on Computing
Integrity constraint checking in stratified databases
Journal of Logic Programming
Optimization, approximation, and complexity classes
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Ambivalent data structures for dynamic 2-edge-connectivity and k smallest spanning trees
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Dynamic expression trees and their applications
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Maintaining views incrementally
SIGMOD '93 Proceedings of the 1993 ACM SIGMOD international conference on Management of data
The complexity of iterated multiplication
Information and Computation
Incremental evaluation of computational circuits
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Incremental Evaluation of Datalog Queries
ICDT '92 Proceedings of the 4th International Conference on Database Theory
On Materializing Views and On-Line Queries
ICDT '92 Proceedings of the 4th International Conference on Database Theory
A Complexity Theoretic Approach to Incremental Computation
STACS '93 Proceedings of the 10th Annual Symposium on Theoretical Aspects of Computer Science
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
On the Relative Complexity of Some Languages in NC 1
On the Relative Complexity of Some Languages in NC 1
View maintenance issues for the chronicle data model (extended abstract)
PODS '95 Proceedings of the fourteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Space-bounded FOIES (extended abstract)
PODS '95 Proceedings of the fourteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
PODS '95 Proceedings of the fourteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Perspectives on database theory
ACM SIGACT News
Deterministic FOIES are strictly weaker
Annals of Mathematics and Artificial Intelligence
ICDT '99 Proceedings of the 7th International Conference on Database Theory
Efficient Incremental Validation of XML Documents
ICDE '04 Proceedings of the 20th International Conference on Data Engineering
Information and Computation
Incremental maintenance of shortest distance and transitive closure in first-order logic and SQL
ACM Transactions on Database Systems (TODS)
Managing RBAC states with transitive relations
ASIACCS '07 Proceedings of the 2nd ACM symposium on Information, computer and communications security
Recency-Abstraction for heap-allocated storage
SAS'06 Proceedings of the 13th international conference on Static Analysis
On the Validation of Invariants at Runtime
Fundamenta Informaticae
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Traditionally, computational complexity has considered only static problems. Classical Complexity Classes such as NC, P, NP, and PSPACE are defined in terms of the complexity of checking—upon presentation of an entire input—whether the input satisfies a certain property.For many, if not most, applications of computers including: databases, text editors, program development, it is more appropriate to model the process as a dynamic one. There is a fairly large object being worked on over a period of time. The object is repeatedly modified by users and computations are performed.Thus a dynamic algorithm for a certain class of queries is one that can maintain an input object, e.g. a database, and process changes to the database as well as answering queries about the current database.Here, we introduce the complexity class, Dynamic First-Order Logic (Dyn-FO). This is the class of properties S, for which there is an algorithm that can perform inserts, deletes and queries from S, such that each unit insert, delete, or query is first-order computable. This corresponds to the sets of properties that can be maintained and queried in first-order logic, i.e. relational calculus, on a relational database.We investigate the complexity class Dyn-FO. We show that many interesting properties are in Dyn-FO including, among others, graph connectivity, k-edge connectivity, and the computation of minimum spanning trees. Furthermore, we show that several NP complete optimization problems admit approximation algorithms in Dyn-FO. Note that none of these problems is in static FO, and this fact has been used to justify increasing the power of query languages beyond first-order. It is thus striking that these problems are indeed dynamic first-order, and thus, were computable in first-order database languages all along.We also define “bounded expansion reductions” which honor dynamic complexity classes. We prove that certain standard complete problems for static complexity classes, such as AGAP for P remain complete via these new reductions. On the other hand, we prove that other such problems including GAP for NL and 1GAP for L are no longer complete via bounded expansion reductions. Furthermore, we show that a version of AGAP called AGAP+ is not in Dyn-FO unless all of P is contained in parallel linear time.Our results shed light on some of the interesting differences between static and dynamic complexity.