Author:
Lee Nian-Ze,Jiang Jie-Hong R.
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 generalize 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.
Publisher
Association for the Advancement of Artificial Intelligence (AAAI)
Cited by
3 articles.
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1. Function Synthesis for Maximizing Model Counting;Lecture Notes in Computer Science;2023-12-30
2. A Resolution Proof System for Dependency Stochastic Boolean Satisfiability;Journal of Automated Reasoning;2023-08-03
3. What’s New In QBF Solving? : (Invited Talk);2022 24th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC);2022-09