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Professor Immerman is one of the key developers of an active research program called descriptive complexity. This area applies logic to computational complexity, discerning strong mathematical structure underlying standard complexity measures. In a striking series of results, Professor Immerman has shown how all important complexity measures have natural descriptive characterizations. Using this characterization of complexity classes, Professor Immerman showed the very surprising result that non-deterministic space is closed under complement. The negation of this result was a common, well-believed conjecture that had stood open for twenty-five years. Robert Szelepcsenyi proved this result independently.
The same tools of descriptive complexity have wide applicability in database theory. For example, Professor Immerman showed that DATALOG expresses exactly the polynomial-time queries. With his students, Professor Immerman has studied "dynamic complexity," the complexity of queries measured by changes to the database, rather than by the size of the database itself. The dynamic complexity class dynFO captures the set of dynamic queries computable by a first-order query language; this corresponds to SQL without aggregation (the ability to count).
In addition, the logical tools that Professor Immerman has developed have deep applicability in static analysis. In a long and continuing series of papers with Tom Reps, Mooly Sagiv, and related students and colleagues, Professor Immerman studies when and how one can reason about reachability, e.g., when one portion of memory is reachable from another via a series of pointers. These methods are used to automatically check the correctness of programs that manipulate data. This aspect of Professor Immerman's research has valuable applications to software including software-defined networks.
The same tools of descriptive complexity have wide applicability in database theory. For example, Professor Immerman showed that DATALOG expresses exactly the polynomial-time queries. With his students, Professor Immerman has studied "dynamic complexity," the complexity of queries measured by changes to the database, rather than by the size of the database itself. The dynamic complexity class dynFO captures the set of dynamic queries computable by a first-order query language; this corresponds to SQL without aggregation (the ability to count).
In addition, the logical tools that Professor Immerman has developed have deep applicability in static analysis. In a long and continuing series of papers with Tom Reps, Mooly Sagiv, and related students and colleagues, Professor Immerman studies when and how one can reason about reachability, e.g., when one portion of memory is reachable from another via a series of pointers. These methods are used to automatically check the correctness of programs that manipulate data. This aspect of Professor Immerman's research has valuable applications to software including software-defined networks.
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CoRR (2024)
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COMPUTER AIDED VERIFICATION (CAV 2021), PT I (2021): 317-340
Thomas Bernardi, Nurit Dor, Anastasia Fedotov, Shelly Grossman,Neil Immerman,Daniel Jackson, Alexander Nutz, Lior Oppenheim, Or Pistiner,Noam Rinetzky, Mooly Sagiv, Marcelo Taube,
semanticscholar(2020)
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Proceedings of the ACM on Programming Languagesno. POPL (2020): 5-29
user-5f8411ab4c775e9685ff56d3(2020)
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user-5ed732bc4c775e09d87b4c18(2020)
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