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This chapter is about the prospect of proving that certain problems do not have logarithmic-space algorithms (are not in L). Results proven in this chapter include PSPACE-completeness and NL-completeness of classic problems, and the counterintuitive theorems PSPACE=NPSPACE and NL=coNL.
This chapter covers a complexity-theoretic perspective on software verification: An efficient verifier wants to be convinced that some computation’s output is correct, given information by a more powerful prover. Interaction (back-and-forth communication between prover and verifier) is surprisingly effective at convincing a verifier with much less computational resources than would be needed without the prover’s help. This is applicable when someone delegates an intensive computation to an untrusted cloud computing service and wants to be convinced the computation was performed correctly. The chapter concludes with the surprising power of zero-knowledge proofs, in which the prover convinces the verifier without revealing any further information.
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