Dependency Stochastic Boolean Satisfiability: A Logical Formalism for NEXPTIME Decision Problems with Uncertainty
Journal
35th AAAI Conference on Artificial Intelligence, AAAI 2021
Journal Volume
5A
Pages
3877-3885
Date Issued
2021
Author(s)
Lee N.-Z
Abstract
Stochastic Boolean Satisfiability (SSAT) is a logical formalism to model decision problems with uncertainty, such as Partially Observable Markov Decision Process (POMDP) for verification of probabilistic systems. SSAT, however, is limited by its descriptive power within the PSPACE complexity class. More complex problems, such as the NEXPTIME-complete Decentralized POMDP (Dec-POMDP), cannot be succinctly encoded with SSAT. To provide a logical formalism of such problems, we extend the Dependency Quantified Boolean Formula (DQBF), a representative problem in the NEXPTIME-complete class, to its stochastic variant, named Dependency SSAT (DSSAT), and show that DSSAT is also NEXPTIME-complete. We demonstrate the potential applications of DSSAT to circuit synthesis of probabilistic and approximate design. Furthermore, to study the descriptive power of DSSAT, we establish a polynomial-time reduction from Dec-POMDP to DSSAT. With the theoretical foundations paved in this work, we hope to encourage the development of DSSAT solvers for potential broad applications. Copyright © 2021, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.
Other Subjects
Artificial intelligence; Boolean algebra; Polynomial approximation; Stochastic models; Stochastic systems; Complexity class; Decentralised; Decision problems; Logical formalism; Modeling decisions; Partially observable Markov decision process; Power; Stochastic boolean satisfiability; Uncertainty; Verification of probabilistic systems; Markov processes
Type
conference paper