Model Counting meets F
            <sub>0</sub>
            Estimation

Pavan, A.; Vinodchandran, N. V.; Bhattacharya, Arnab; Meel, Kuldeep S.

doi:10.1145/3452021.3458311

Cited by 3 publications

(1 citation statement)

References 52 publications

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“…Finally, we conclude in Section 6. Due to space constraints, many of the involved proofs are omitted and will appear in the full version (Pavan et al 2023) 2 Preliminaries…”

Section: Our Resultsmentioning

confidence: 99%

Constraint Optimization over Semirings

Pavan

Meel

Vinodchandran

et al. 2023

AAAI

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Interpretations of logical formulas over semirings (other than the Boolean semiring) have applications in various areas of computer science including logic, AI, databases, and security. Such interpretations provide richer information beyond the truth or falsity of a statement. Examples of such semirings include Viterbi semiring, min-max or access control semiring, tropical semiring, and fuzzy semiring. The present work investigates the complexity of constraint optimization problems over semirings. The generic optimization problem we study is the following: Given a propositional formula phi over n variable and a semiring (K,+, . ,0,1), find the maximum value over all possible interpretations of phi over K. This can be seen as a generalization of the well-known satisfiability problem (a propositional formula is satisfiable if and only if the maximum value over all interpretations/assignments over the Boolean semiring is 1). A related problem is to find an interpretation that achieves the maximum value. In this work, we first focus on these optimization problems over the Viterbi semiring, which we call optConfVal and optConf. We first show that for general propositional formulas in negation normal form, optConfVal and optConf are in FP^NP. We then investigate optConf when the input formula phi is represented in the conjunctive normal form. For CNF formulae, we first derive an upper bound on the value of optConf as a function of the number of maximum satisfiable clauses. In particular, we show that if r is the maximum number of satisfiable clauses in a CNF formula with m clauses, then its optConf value is at most 1/4^(m-r). Building on this we establish that optConf for CNF formulae is hard for the complexity class FP^NP[log]. We also design polynomial-time approximation algorithms and establish an inapproximability for optConfVal. We establish similar complexity results for these optimization problems over other semirings including tropical, fuzzy, and access control semirings.

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“…Finally, we conclude in Section 6. Due to space constraints, many of the involved proofs are omitted and will appear in the full version (Pavan et al 2023) 2 Preliminaries…”

Section: Our Resultsmentioning

confidence: 99%

Constraint Optimization over Semirings

Pavan

Meel

Vinodchandran

et al. 2023

AAAI

View full text Add to dashboard Cite

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Estimating the Size of Union of Sets in Streaming Models

Meel

Vinodchandran

Chakraborty

2021

Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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Model Counting Meets F ₀ Estimation

Pavan

Vinodchandran

Bhattacharyya

et al. 2023

ACM Trans. Database Syst.

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Constraint satisfaction problems (CSP’s) and data stream models are two powerful abstractions to capture a wide variety of problems arising in different domains of computer science. Developments in the two communities have mostly occurred independently and with little interaction between them. In this work, we seek to investigate whether bridging the seeming communication gap between the two communities may pave the way to richer fundamental insights. To this end, we focus on two foundational problems: model counting for CSP’s and computation of zeroth frequency moments ( F 0 ) for data streams. Our investigations lead us to observe a striking similarity in the core techniques employed in the algorithmic frameworks that have evolved separately for model counting and F 0 computation. We design a recipe for translating algorithms developed for F 0 estimation to model counting, resulting in new algorithms for model counting. We also provide a recipe for transforming sampling algorithm over streams to constraint sampling algorithms. We then observe that algorithms in the context of distributed streaming can be transformed into distributed algorithms for model counting. We next turn our attention to viewing streaming from the lens of counting and show that framing F 0 estimation as a special case of #DNF counting allows us to obtain a general recipe for a rich class of streaming problems, which had been subjected to case-specific analysis in prior works. In particular, our view yields an algorithm for multidimensional range efficient F 0 estimation with a simpler analysis.

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Model Counting meets F ₀ Estimation

Cited by 3 publications

References 52 publications

Constraint Optimization over Semirings

Constraint Optimization over Semirings

Estimating the Size of Union of Sets in Streaming Models

Model Counting Meets F ₀ Estimation

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Model Counting meets F 0 Estimation

Cited by 3 publications

References 52 publications

Constraint Optimization over Semirings

Constraint Optimization over Semirings

Estimating the Size of Union of Sets in Streaming Models

Model Counting Meets F 0 Estimation

Contact Info

Product

Resources

About

Model Counting meets F ₀ Estimation

Model Counting Meets F ₀ Estimation