3 research outputs found
Dependency Stochastic Boolean Satisfiability: A Logical Formalism for NEXPTIME Decision Problems with Uncertainty
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.Comment: 10 pages, 5 figures. A condensed version of this work is published in
the AAAI Conference on Artificial Intelligence (AAAI) 202
Justicia: A Stochastic SAT Approach to Formally Verify Fairness
As a technology ML is oblivious to societal good or bad, and thus, the field
of fair machine learning has stepped up to propose multiple mathematical
definitions, algorithms, and systems to ensure different notions of fairness in
ML applications. Given the multitude of propositions, it has become imperative
to formally verify the fairness metrics satisfied by different algorithms on
different datasets. In this paper, we propose a \textit{stochastic
satisfiability} (SSAT) framework, Justicia, that formally verifies different
fairness measures of supervised learning algorithms with respect to the
underlying data distribution. We instantiate Justicia on multiple
classification and bias mitigation algorithms, and datasets to verify different
fairness metrics, such as disparate impact, statistical parity, and equalized
odds. Justicia is scalable, accurate, and operates on non-Boolean and compound
sensitive attributes unlike existing distribution-based verifiers, such as
FairSquare and VeriFair. Being distribution-based by design, Justicia is more
robust than the verifiers, such as AIF360, that operate on specific test
samples. We also theoretically bound the finite-sample error of the verified
fairness measure.Comment: 24 pages, 7 figures, 5 theorem