Descriptive complexity of real computation and probabilistic independence logic
Abstract
We introduce a novel variant of BSS machines called Separate Branching BSS machines (SBSS in short) and develop a Fagintype logical characterisation for languages decidable in nondeterministic polynomial time by SBSS machines. We show that NP on SBSS machines is strictly included in NP on BSS machines and that every NP language on SBSS machines is a countable union of closed sets in the usual topology of R^n. Moreover, we establish that on Boolean inputs NP on SBSS machines without real constants characterises a natural fragment of the complexity class existsR (a class of problems polynomial time reducible to the true existential theory of the reals) and hence lies between NP and PSPACE. Finally we apply our results to determine the data complexity of probabilistic independence logic.
 Publication:

arXiv eprints
 Pub Date:
 March 2020
 arXiv:
 arXiv:2003.00644
 Bibcode:
 2020arXiv200300644H
 Keywords:

 Computer Science  Logic in Computer Science;
 Computer Science  Computational Complexity;
 Mathematics  Logic