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Sravanthi Chede

Publications and source records attributed to Sravanthi Chede.

5 recordsLinked to original sources
arXiv2026

On Proof Systems for #QBF

For a quantified Boolean formula (QBF), the problem of computing the number of winning strategies is known as the #QBF problem. This problem is considered harder than the analogous #SAT problem. Recently, important proof systems for QBFs and #SAT have been studied. By extending the ideas from both fields, we show that it is possible to design proof systems for #QBF. Such proof systems are important not only for advancing the theory of #QBF but also for certifying and designing better #QBF solvers, an area that is still in its early stages. In this paper, we explore #QBF proof systems to count the number of Skolem functions. Apart from a naive system, we study #QBF systems based on the expansion rule of universal variables in QBFs. We observe that these systems have inherent structural weaknesses that lead to lower bounds. As an alternative, we propose a #QBF proof system that we call Q-MICE, which consists of sound inference rules for computing and certifying the #QBF solution, similar to the line-based #SAT proof system MICE. To demonstrate the strength of Q-MICE, we present various upper bounds, such as the quantified version of the propositional XOR-PAIRS formula, which are known to be hard for MICE. Consequently, we also separate Q-MICE from the expansion-based #QBF proof systems.

cs.LO↗
arXiv2021

Extending Merge Resolution to a Family of Proof Systems

Merge Resolution (MRes [Beyersdorff et al. J. Autom. Reason.'2021]) is a recently introduced proof system for false QBFs. It stores the countermodels as merge maps. Merge maps are deterministic branching programs in which isomorphism checking is efficient making MRes a polynomial time verifiable proof system. In this paper, we introduce a family of proof systems MRes-R in which, the countermodels are stored in any pre-fixed complete representation R, instead of merge maps. Hence corresponding to each such R, we have a sound and refutationally complete QBF-proof system in MRes-R. To handle arbitrary representations for the strategies, we introduce consistency checking rules in MRes-R instead of isomorphism checking. As a result these proof systems are not polynomial time verifiable. Consequently, the paper shows that using merge maps is too restrictive and can be replaced with arbitrary representations leading to several interesting proof systems. Exploring proof theoretic properties of MRes-R, we show that eFrege+$\forall$red simulates all valid refutations from proof systems in MRes-R. In order to simulate arbitrary representations in MRes-R, we first represent the steps used by the proof systems as a new complete structure. Consequently, the corresponding proof system belonging to MRes-R is able to simulate all proof systems in MRes-R. Finally, we simulate this proof system via eFrege+$\forall$red using the ideas from [Chew et al. ECCC.'2021]. On the lower bound side, we show that the completion principle formulas from [Jonata et al. Theor. Comput. Sci.'2015] which are shown to be hard for regular MRes in [Beyersdorff et al. FSTTCS.'2020], are also hard for any regular proof system in MRes-R. Thereby, the paper lifts the lower bound of regular MRes to an entire class of proof systems, which use some complete representation, including those undiscovered, instead of merge maps.

cs.CC↗
arXiv2021

World War III Analysis using Signed Social Networks

In the recent period of time with a lot of social platforms emerging, the relationships among various units can be framed with respect to either positive, negative or no relation. These units can be individuals, countries or others that form the basic structural component of a signed network. These signed networks picture a dynamic characteristic of the graph so formed allowing only few combinations of signs that brings the structural balance theorem in picture. Structural balance theory affirms that signed social networks tend to be organized so as to avoid conflictual situations, corresponding to cycles of unstable relations. The aim of structural balance in networks is to find proper partitions of nodes that guarantee equilibrium in the system allowing only few combination triangles with signed edges to be permitted in graph. Most of the works in this field of networking have either explained the importance of signed graph or have applied the balance theorem and tried to solve problems. Following the recent time trends with each nation emerging to be superior and competing to be the best, the probable doubt of happening of WW-III(World War-III) comes into every individuals mind. Nevertheless, our paper aims at answering some of the interesting questions on World War-III. In this project we have worked with the creation of a signed graph picturing the World War-III participating countries as nodes and have predicted the best possible coalition of countries that will be formed during war. Also, we have visually depicted the number of communities that will be formed in this war and the participating countries in each communities.

cs.SI↗
arXiv2021

QRAT Polynomially Simulates Merge Resolution

Merge Resolution (MRes [Beyersdorff et al. J. Autom. Reason.'2021] ) is a refutational proof system for quantified Boolean formulas (QBF). Each line of MRes consists of clauses with only existential literals, together with information of countermodels stored as merge maps. As a result, MRes has strategy extraction by design. The QRAT [Heule et al. J. Autom. Reason.'2017] proof system was designed to capture QBF preprocessing. QRAT can simulate both the expansion-based proof system $\forall$Exp+Res and CDCL-based QBF proof system LD-Q-Res. A family of false QBFs called SquaredEquality formulas were introduced in [Beyersdorff et al. J. Autom. Reason.'2021] and shown to be easy for MRes but need exponential size proofs in Q-Res, QU-Res, CP+$\forall$red, $\forall$Exp+Res, IR-calc and reductionless LD-Q-Res. As a result none of these systems can simulate MRes. In this paper, we show a short QRAT refutation of the SquaredEquality formulas. We further show that QRAT strictly p-simulates MRes. Besides highlighting the power of QRAT system, this work also presents the first simulation result for MRes.

cs.CC↗