Related papers: A Proof Checking View of Parameterized Complexity
We survey a collective achievement of a group of researchers: the PCP Theorems. They give new definitions of the class \np, and imply that computing approximate solutions to many \np-hard problems is itself \np-hard. Techniques developed to…
The subject logic in computer science should entail proof theoretic applications. So the question arises whether open problems in computational complexity can be solved by advanced proof theoretic techniques. In particular, consider the…
We investigate the problem of safety verification of infinite-state parameterized programs that are formed based on a rich class of topologies. We introduce a new proof system, called parametric proof spaces, which exploits the underlying…
Motivated by the inapproximability of reconfiguration problems, we present a new PCP-type characterization of PSPACE, which we call a probabilistically checkable reconfiguration proof (PCRP): Any PSPACE computation can be encoded into an…
We initiate a program of parameterized proof complexity that aims to provide evidence that FPT is different from W[1]. A similar program already exists for the classes W[2] and W[SAT]. We contrast these programs and prove upper and lower…
We present several known formalizations of theorems from computational complexity in bounded arithmetic and formalize the PCP theorem in the theory PV1 (no formalization of this theorem was known). This includes a formalization of the…
We survey results on the formalization and independence of mathematical statements related to major open problems in computational complexity theory. Our primary focus is on recent findings concerning the (un)provability of complexity…
A PCP is a proof system for NP in which the proof can be checked by a probabilistic verifier. The verifier is only allowed to read a very small portion of the proof, and in return is allowed to err with some bounded probability. The…
We present a new distributed model of probabilistically checkable proofs (PCP). A satisfying assignment $x \in \{0,1\}^n$ to a CNF formula $\varphi$ is shared between two parties, where Alice knows $x_1, \dots, x_{n/2}$, Bob knows…
We introduce a 2-round stochastic constraint-satisfaction problem, and show that its approximation version is complete for (the promise version of) the complexity class AM. This gives a `PCP characterization' of AM analogous to the PCP…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
Coding theory is very useful for real world applications. A notable example is digital television. Basically, coding theory is to study a way of detecting and/or correcting data that may be true or false. Moreover coding theory is an area…
The emergence of tools based on artificial intelligence has also led to the need of producing explanations which are understandable by a human being. In most approaches, the system is considered a black box, making it difficult to generate…
This paper shows that a variety of software model-checking algorithms can be seen as proof-search strategies for a non-standard proof system, known as a cyclic proof system. Our use of the cyclic proof system as a logical foundation of…
The relationship between the complexity classes P and NP is a question that has not yet been answered by the Theory of Computation. The existence of a language in NP, proven not to belong to P, is sufficient evidence to establish the…
We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…
Proving programs terminating is a fundamental computer science challenge. Recent research has produced powerful tools that can check a wide range of programs for termination. The analog for probabilistic programs, namely termination with…
Couplings are a powerful mathematical tool for reasoning about pairs of probabilistic processes. Recent developments in formal verification identify a close connection between couplings and pRHL, a relational program logic motivated by…
Parameterized complexity enables the practical solution of generally intractable NP-hard problems when certain parameters are small, making it particularly useful in real-world applications. The study of string problems in this framework…
Teaching proofs is a crucial component of any undergraduate-level program that covers formal reasoning. We have developed a calculational reasoning format and refined it over several years of teaching a freshman-level course, "Logic and…