Dyn-FO: A Parallel, Dynamic Complexity Class

Patnaik, Sushant; Immerman, Neil

doi:10.1006/jcss.1997.1520

Cited by 81 publications

(170 citation statements)

References 28 publications

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“…Already with the introduction of the dynamic complexity framework, dynamic first-order programs for maintaining the reachability query for acyclic and undirected graphs have been known [DS95,PI97]. Later Hesse showed that reachability (on arbitrary graphs) can be maintained using TC 0 -circuits as update mechanism [Hes03a], where TC 0 -circuits are defined like AC 0 -circuits except that they can also use majority gates.…”

Section: Maintainability Of Basic Queriesmentioning

confidence: 99%

“…Already Patnaik and Immerman observed that regular languages can be maintained in DynFO [PI97]. A more extensive study of languages conducted by Gelade, Marquardt and Schwentick revealed that regular languages are exactly the languages that can be maintained in DynProp [GMS12].…”

Section: Maintainability Of Basic Queriesmentioning

confidence: 99%

“…Among them notions of reducibility and complete problems for dynamic complexity classes [PI97,HI02,WS07], the (in)dependence of the auxiliary relations from the actual input relations [DS97,DS98,GS12], and the relation of dynamic and static complexity classes [PI94,Ete98,WS07,GMS12]. For a detailed overview over the latter aspect we refer to Chapter 3.…”

Section: Maintainability Of Basic Queriesmentioning

confidence: 99%

“…Therefore classes with logarithmic space and time updates (on random access machines) have been studied in [MSVT94]. Some of the constructions and reduction concepts from [MSVT94] have been reused by Patnaik and Immerman in [PI97].…”

Section: Theory Of Incremental Computationmentioning

confidence: 99%

“…This setting was independently formalized by Dong, Su and Topor [DT92,DS93] and Patnaik and Immerman [PI94]. Both formalizations are very similar.…”

Section: Introductionmentioning

confidence: 98%

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Small Dynamic Complexity Classes

Zeume

2017

Lecture Notes in Computer Science

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Everything changes and nothing stands still. -Heraclitus (quoted by Platon in Cratylus) PrefaceOn the first few days of my PhD studies in the summer of 2009, my adviser Thomas Schwentick introduced me to dynamic complexity. Very recently Wouter Gelade, Marcel Marquardt and Thomas had obtained a very nice characterization of regular languages in terms of dynamic complexity, and also a lower bound for the dynamic complexity of the alternating reachability problem. Many interesting problems in this area seemed to wait for a solution; and so I started to try to prove a lower bound for reachability. I was not successful. After two (at the end frustrating) months, I abandoned this project.In the following two and a half years I almost forgot about dynamic complexity. Decidability issues for the two-variable fragment of first-order logic had turned out to be a much more accessible and fruitful field. Thomas and I had obtained several results, and a PhD in this field seemed not to be too far away. This was the moment when Thomas asked whether I would be interested in applying for funds from the DFG. If successful, such funding could relieve me from my teaching obligations.We decided to have a second, deeper look into dynamic complexity, and to apply for funds for doing an extensive study of the power of logics in dynamic settings. At that time, the decision to spend more time on dynamic complexity was not easy for me. I was in the third year of my PhD and already had results and further ideas for two-variable logics; and it was not clear whether an application for funding would be successful. On the other hand, now I had more experience, which might turn out to be helpful to attack the very same problems that I had tried to solve at the beginning of my PhD. I do not regret the decision.With the thesis at hand I want to document the progress in dynamic complexity that we have made in the last two and a half years. The focus of this thesis is on small dynamic descriptive complexity classes, in particular on lower bound methods for them. A short summary of results on decidability issues for two-variable logic is presented at the end of the thesis.

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Section: Maintainability Of Basic Queriesmentioning

confidence: 99%

Section: Maintainability Of Basic Queriesmentioning

confidence: 99%

Section: Maintainability Of Basic Queriesmentioning

confidence: 99%

Section: Theory Of Incremental Computationmentioning

confidence: 99%

“…This setting was independently formalized by Dong, Su and Topor [DT92,DS93] and Patnaik and Immerman [PI94]. Both formalizations are very similar.…”

Section: Introductionmentioning

confidence: 98%

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Small Dynamic Complexity Classes

Zeume

2017

Lecture Notes in Computer Science

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Adding For-Loops to First-Order Logic

Neven¹,

Otto

Tyszkiewicz

et al. 2001

Information and Computation

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This paper shows how to harness existing theorem provers for first-order logic to automatically verify safety properties of imperative programs that perform dynamic storage allocation and destructive updating of pointer-valued structure fields. One of the main obstacles is specifying and proving the (absence) of reachability properties among dynamically allocated cells. The main technical contributions are methods for simulating reachability in a conservative way using first-order formulas-the formulas describe a superset of the set of program states that can actually arise. These methods are employed for semi-automatic program verification (i.e., using programmer-supplied loop invariants) on programs such as mark-and-sweep garbage collection and destructive reversal of a singly linked list. (The mark-and-sweep example has been previously reported as being beyond the capabilities of ESC/Java.

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Arity Bounds in First-Order Incremental Evaluation and Definition of Polynomial Time Database Queries

Dong

1998

Journal of Computer and System Sciences

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After inserting a tuple into or deleting a tuple from a database, a firstorder incremental evaluation system (or a``foies'') for a database query derives the new query answer by using a first-order query on the new database, the old answer, and perhaps some stored auxiliary relations. Moreover, the auxiliary relations must also be maintained similarly using first-order queries.In this paper we measure the space needed by foies in terms of the maximal arity of the auxiliary relations and present results on the existence and nonexistence of such space-restricted foies for a variety of graph queries, including counting and transitive closure. We construct space efficient foies for these queries and show that the arity bounds are tight using Ehrenfeucht Fra@ sse games. In particular, for transitive closure over undirected graphs, the minimum arity bound of its foies is shown to be exactly two; this resolves an open problem raised by Patnaik and Immerman in 1994. For the general case, we show that the arity-based hierarchy is strict for all arities. The strictness proof uses queries with input relations having arities much larger than the auxiliary relations. It is still open whether the hierarchy remains strict for arities two or greater when the input relations of queries have arities bounded by a fixed number, such as two, or by the arities of the auxiliary relations.Finally, we consider a variation of foies where the cost of storing the answer to the query is also``charged.'' We show that the arity hierarchy in this case is also strict. The positions of queries in the two arity-based hierarchies can differ; we give the positions in this hierarchy of the queries considered for the other arity hierarchy. ]

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Dyn-FO: A Parallel, Dynamic Complexity Class

Cited by 81 publications

References 28 publications

Small Dynamic Complexity Classes

Small Dynamic Complexity Classes

Adding For-Loops to First-Order Logic

Arity Bounds in First-Order Incremental Evaluation and Definition of Polynomial Time Database Queries

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