Related papers: $\rm P$ has polynomial-time finite-state verifiers
This paper is our second step towards developing a theory of testing monomials in multivariate polynomials. The central question is to ask whether a polynomial represented by an arithmetic circuit has some types of monomials in its…
In this paper, we develop a quantified propositional proof systems that corresponds to logarithmic-space reasoning. We begin by defining a class SigmaCNF(2) of quantified formulas that can be evaluated in log space. Then our new proof…
In classical complexity theory, the two definitions of probabilistically checkable proofs -- the constraint satisfaction and the nonlocal games version -- are computationally equal in power. In the quantum setting, the situation is far less…
Rational verification refers to the problem of checking which temporal logic properties hold of a concurrent multiagent system, under the assumption that agents in the system choose strategies that form a game-theoretic equilibrium.…
Differential privacy is a promising approach to privacy preserving data analysis with a well-developed theory for functions. Despite recent work on implementing systems that aim to provide differential privacy, the problem of formally…
Publicly verifiable quantum money is a protocol for the preparation of quantum states that can be efficiently verified by any party for authenticity but is computationally infeasible to counterfeit. We develop a cryptographic scheme for…
We survey some results on the automatic verification of parameterized programs without identities. These are systems composed of arbitrarily many components, all of them running exactly the same finite-state program. We discuss the…
One-time programs, computer programs which self-destruct after being run only once, are a powerful building block in cryptography and would allow for new forms of secure software distribution. However, ideal one-time programs have been…
We study finite-state transducers and their power for transforming infinite words. Infinite sequences of symbols are of paramount importance in a wide range of fields, from formal languages to pure mathematics and physics. While finite…
A program invariant is a property that holds for every execution of the program. Recent work suggest to infer likely-only invariants, via dynamic analysis. A likely invariant is a property that holds for some executions but is not…
Pseudorandom quantum states (PRSs) and pseudorandom unitaries (PRUs) possess the dual nature of being efficiently constructible while appearing completely random to any efficient quantum algorithm. In this study, we establish fundamental…
An efficient randomized polynomial identity test for noncommutative polynomials given by noncommutative arithmetic circuits remains an open problem. The main bottleneck to applying known techniques is that a noncommutative circuit of size…
In a quantum money scheme, a bank can issue money that users cannot counterfeit. Similar to bills of paper money, most quantum money schemes assign a unique serial number to each money state, thus potentially compromising the privacy of the…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
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…
We give new proofs of soundness (all representable functions on base types lies in certain complexity classes) for Elementary Affine Logic, LFPL (a language for polytime computation close to realistic functional programming introduced by…
In Formal Languages and Automata Theory courses, students find understanding nondeterministic finite-state and pushdown automata difficult. In many cases, this means that it is challenging for them to comprehend the operational semantics of…
Despite significant developments in Proof Theory, surprisingly little attention has been devoted to the concept of proof verifier. In particular, the mathematical community may be interested in studying different types of proof verifiers…
Characterizing increasingly complex quantum systems is a central task in quantum information science, yet experimental costs often scale prohibitively with system size. Certifying key properties using simple local measurements is highly…
Large Language Models (LLMs) are extensively used today across various sectors, including academia, research, business, and finance, for tasks such as text generation, summarization, and translation. Despite their widespread adoption, these…