160 research outputs found
Fine-grained Complexity Meets IP = PSPACE
In this paper we study the fine-grained complexity of finding exact and
approximate solutions to problems in P. Our main contribution is showing
reductions from exact to approximate solution for a host of such problems.
As one (notable) example, we show that the Closest-LCS-Pair problem (Given
two sets of strings and , compute exactly the maximum with ) is equivalent to its approximation version
(under near-linear time reductions, and with a constant approximation factor).
More generally, we identify a class of problems, which we call BP-Pair-Class,
comprising both exact and approximate solutions, and show that they are all
equivalent under near-linear time reductions.
Exploring this class and its properties, we also show:
Under the NC-SETH assumption (a significantly more relaxed
assumption than SETH), solving any of the problems in this class requires
essentially quadratic time.
Modest improvements on the running time of known algorithms
(shaving log factors) would imply that NEXP is not in non-uniform
.
Finally, we leverage our techniques to show new barriers for
deterministic approximation algorithms for LCS.
At the heart of these new results is a deep connection between interactive
proof systems for bounded-space computations and the fine-grained complexity of
exact and approximate solutions to problems in P. In particular, our results
build on the proof techniques from the classical IP = PSPACE result
Strong ETH Breaks With Merlin and Arthur: Short Non-Interactive Proofs of Batch Evaluation
We present an efficient proof system for Multipoint Arithmetic Circuit
Evaluation: for every arithmetic circuit of size and
degree over a field , and any inputs ,
the Prover sends the Verifier the values and a proof of length, and
the Verifier tosses coins and can check the proof in about time, with probability of error less than .
For small degree , this "Merlin-Arthur" proof system (a.k.a. MA-proof
system) runs in nearly-linear time, and has many applications. For example, we
obtain MA-proof systems that run in time (for various ) for the
Permanent, Circuit-SAT for all sublinear-depth circuits, counting
Hamiltonian cycles, and infeasibility of - linear programs. In general,
the value of any polynomial in Valiant's class can be certified
faster than "exhaustive summation" over all possible assignments. These results
strongly refute a Merlin-Arthur Strong ETH and Arthur-Merlin Strong ETH posed
by Russell Impagliazzo and others.
We also give a three-round (AMA) proof system for quantified Boolean formulas
running in time, nearly-linear time MA-proof systems for
counting orthogonal vectors in a collection and finding Closest Pairs in the
Hamming metric, and a MA-proof system running in -time for
counting -cliques in graphs.
We point to some potential future directions for refuting the
Nondeterministic Strong ETH.Comment: 17 page
IaaS-cloud security enhancement: an intelligent attribute-based access control model and implementation
The cloud computing paradigm introduces an efficient utilisation of huge computing
resources by multiple users with minimal expense and deployment effort
compared to traditional computing facilities. Although cloud computing has incredible
benefits, some governments and enterprises remain hesitant to transfer
their computing technology to the cloud as a consequence of the associated security
challenges. Security is, therefore, a significant factor in cloud computing
adoption. Cloud services consist of three layers: Software as a Service (SaaS), Platform
as a Service (PaaS), and Infrastructure as a Service (IaaS). Cloud computing
services are accessed through network connections and utilised by multi-users who
can share the resources through virtualisation technology. Accordingly, an efficient
access control system is crucial to prevent unauthorised access.
This thesis mainly investigates the IaaS security enhancement from an access
control point of view. [Continues.
LTLf and LDLf Monitoring: A Technical Report
Runtime monitoring is one of the central tasks to provide operational
decision support to running business processes, and check on-the-fly whether
they comply with constraints and rules. We study runtime monitoring of
properties expressed in LTL on finite traces (LTLf) and in its extension LDLf.
LDLf is a powerful logic that captures all monadic second order logic on finite
traces, which is obtained by combining regular expressions and LTLf, adopting
the syntax of propositional dynamic logic (PDL). Interestingly, in spite of its
greater expressivity, LDLf has exactly the same computational complexity of
LTLf. We show that LDLf is able to capture, in the logic itself, not only the
constraints to be monitored, but also the de-facto standard RV-LTL monitors.
This makes it possible to declaratively capture monitoring metaconstraints, and
check them by relying on usual logical services instead of ad-hoc algorithms.
This, in turn, enables to flexibly monitor constraints depending on the
monitoring state of other constraints, e.g., "compensation" constraints that
are only checked when others are detected to be violated. In addition, we
devise a direct translation of LDLf formulas into nondeterministic automata,
avoiding to detour to Buechi automata or alternating automata, and we use it to
implement a monitoring plug-in for the PROM suite
Complexity Theory
Computational Complexity Theory is the mathematical study of the intrinsic power and limitations of computational resources like time, space, or randomness. The current workshop focused on recent developments in various sub-areas including arithmetic complexity, Boolean complexity, communication complexity, cryptography, probabilistic proof systems, pseudorandomness, and quantum computation. Many of the developments are related to diverse mathematical fields such as algebraic geometry, combinatorial number theory, probability theory, representation theory, and the theory of error-correcting codes
Quantum Merlin-Arthur proof systems for synthesizing quantum states
Complexity theory typically focuses on the difficulty of solving
computational problems using classical inputs and outputs, even with a quantum
computer. In the quantum world, it is natural to apply a different notion of
complexity, namely the complexity of synthesizing quantum states. We
investigate a state-synthesizing counterpart of the class NP, referred to as
stateQMA, which is concerned with preparing certain quantum states through a
polynomial-time quantum verifier with the aid of a single quantum message from
an all-powerful but untrusted prover. This is a subclass of the class stateQIP
recently introduced by Rosenthal and Yuen (ITCS 2022), which permits
polynomially many interactions between the prover and the verifier. Our main
result consists of error reduction of this class and its variants with an
exponentially small gap or a bounded space, as well as how this class relates
to other fundamental state synthesizing classes, i.e., states generated by
uniform polynomial-time quantum circuits (stateBQP) and space-uniform
polynomial-space quantum circuits (statePSPACE). Furthermore, we establish that
the family of UQMA witnesses, considered as one of the most natural candidates,
is in stateQMA. Additionally, we demonstrate that stateQCMA achieves perfect
completeness.Comment: 31 pages. v2: minor changes. v3: add a new result - UQMA witness
family is in stateQM
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