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DynFO: A Parallel, Dynamic Complexity Class
 Journal of Computer and System Sciences
, 1994
"... Traditionally, computational complexity has considered only static problems. Classical Complexity Classes such as NC, P, and NP are defined in terms of the complexity of checking  upon presentation of an entire input  whether the input satisfies a certain property. For many applications of compu ..."
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Cited by 50 (4 self)
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Traditionally, computational complexity has considered only static problems. Classical Complexity Classes such as NC, P, and NP are defined in terms of the complexity of checking  upon presentation of an entire input  whether the input satisfies a certain property. For many applications of computers 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. We develop a theory of Dynamic Complexity. We study the new complexity class, Dynamic FirstOrder Logic (DynFO). This is the set of properties that can be maintained and queried in firstorder logic, i.e. relational calculus, on a relational database. We show that many interesting properties are in DynFO including multiplication, graph connectivity, bipartiteness, and the computation of minimum spanning trees. Note that none of these problems is in static FO, and this f...
A FirstOrder Isomorphism Theorem
 SIAM JOURNAL ON COMPUTING
, 1993
"... We show that for most complexity classes of interest, all sets complete under firstorder projections are isomorphic under firstorder isomorphisms. That is, a very restricted version of the BermanHartmanis Conjecture holds. ..."
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Cited by 24 (5 self)
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We show that for most complexity classes of interest, all sets complete under firstorder projections are isomorphic under firstorder isomorphisms. That is, a very restricted version of the BermanHartmanis Conjecture holds.
Model Expansion as a Framework for Modelling and Solving Search Problems
"... We propose a framework for modelling and solving search problems using logic, and describe a project whose goal is to produce practically effective, general purpose tools for representing and solving search problems based on this framework. The mathematical foundation lies in the areas of finite mod ..."
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Cited by 3 (3 self)
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We propose a framework for modelling and solving search problems using logic, and describe a project whose goal is to produce practically effective, general purpose tools for representing and solving search problems based on this framework. The mathematical foundation lies in the areas of finite model theory and descriptive complexity, which provide us with many classical results, as well as powerful techniques, not available to many other approaches with similar goals. We describe the mathematical foundations; explain an extension to classical logic with inductive definitions that we consider central; give a summary of complexity and expressiveness properties; describe an approach to implementing solvers based on grounding; present grounding algorithms based on an extension of the relational algebra; describe an implementation of our framework which includes use of inductive definitions, sorts and order; and give experimental results comparing the performance of our implementation with ASP solvers and another solver based on the same framework. 1.
An Attempt to Automate NPHardness Reductions via SO∃ Logic
, 2004
"... We explore the possibility of automating NPhardness reductions. We motivate the problem from an artificial intelligence perspective, then propose the use of secondorder existential (SO#) logic as representation language for decision problems. Building upon the theoretical framework of J. Antonio ..."
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We explore the possibility of automating NPhardness reductions. We motivate the problem from an artificial intelligence perspective, then propose the use of secondorder existential (SO#) logic as representation language for decision problems. Building upon the theoretical framework of J. Antonio Medina, we explore the possibility of implementing seven syntactic operators. Each operator transforms SO# sentences in a way that preserves NPcompleteness. We subsequently propose a program which implements these operators.