1,474 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Folding interpretations
We study the polyregular string-to-string functions, which are certain
functions of polynomial output size that can be described using automata and
logic. We describe a system of combinators that generates exactly these
functions. Unlike previous systems, the present system includes an iteration
mechanism, namely fold. Although unrestricted fold can define all primitive
recursive functions, we identify a type system (inspired by linear logic) that
restricts fold so that it defines exactly the polyregular functions. We also
present related systems, for quantifier-free functions as well as for linear
regular functions on both strings and trees.Comment: Author's version of a LICS 23 pape
Current and Future Challenges in Knowledge Representation and Reasoning
Knowledge Representation and Reasoning is a central, longstanding, and active
area of Artificial Intelligence. Over the years it has evolved significantly;
more recently it has been challenged and complemented by research in areas such
as machine learning and reasoning under uncertainty. In July 2022 a Dagstuhl
Perspectives workshop was held on Knowledge Representation and Reasoning. The
goal of the workshop was to describe the state of the art in the field,
including its relation with other areas, its shortcomings and strengths,
together with recommendations for future progress. We developed this manifesto
based on the presentations, panels, working groups, and discussions that took
place at the Dagstuhl Workshop. It is a declaration of our views on Knowledge
Representation: its origins, goals, milestones, and current foci; its relation
to other disciplines, especially to Artificial Intelligence; and on its
challenges, along with key priorities for the next decade
Bounded Relativization
Relativization is one of the most fundamental concepts in complexity theory, which explains the difficulty of resolving major open problems. In this paper, we propose a weaker notion of relativization called bounded relativization. For a complexity class ?, we say that a statement is ?-relativizing if the statement holds relative to every oracle ? ? ?. It is easy to see that every result that relativizes also ?-relativizes for every complexity class ?. On the other hand, we observe that many non-relativizing results, such as IP = PSPACE, are in fact PSPACE-relativizing.
First, we use the idea of bounded relativization to obtain new lower bound results, including the following nearly maximum circuit lower bound: for every constant ? > 0, BPE^{MCSP}/2^{?n} ? SIZE[2?/n].
We prove this by PSPACE-relativizing the recent pseudodeterministic pseudorandom generator by Lu, Oliveira, and Santhanam (STOC 2021).
Next, we study the limitations of PSPACE-relativizing proof techniques, and show that a seemingly minor improvement over the known results using PSPACE-relativizing techniques would imply a breakthrough separation NP ? L. For example:
- Impagliazzo and Wigderson (JCSS 2001) proved that if EXP ? BPP, then BPP admits infinitely-often subexponential-time heuristic derandomization. We show that their result is PSPACE-relativizing, and that improving it to worst-case derandomization using PSPACE-relativizing techniques implies NP ? L.
- Oliveira and Santhanam (STOC 2017) recently proved that every dense subset in P admits an infinitely-often subexponential-time pseudodeterministic construction, which we observe is PSPACE-relativizing. Improving this to almost-everywhere (pseudodeterministic) or (infinitely-often) deterministic constructions by PSPACE-relativizing techniques implies NP ? L.
- Santhanam (SICOMP 2009) proved that pr-MA does not have fixed polynomial-size circuits. This lower bound can be shown PSPACE-relativizing, and we show that improving it to an almost-everywhere lower bound using PSPACE-relativizing techniques implies NP ? L.
In fact, we show that if we can use PSPACE-relativizing techniques to obtain the above-mentioned improvements, then PSPACE ? EXPH. We obtain our barrier results by constructing suitable oracles computable in EXPH relative to which these improvements are impossible
Multirole Logic and Multiparty Channels
We identify multirole logic as a new form of logic in which
conjunction/disjunction is interpreted as an ultrafilter on some underlying set
of roles and the notion of negation is generalized to endomorphisms on this
set. We formulate both multirole logic (MRL) and linear multirole logic (LMRL)
as natural generalizations of classical logic (CL) and classical linear logic
(CLL), respectively. Among various meta-properties established for MRL and
LMRL, we obtain one named multiparty cut-elimination stating that every cut
involving one or more sequents (as a generalization of a binary cut involving
exactly two sequents) can be eliminated, thus extending the celebrated result
of cut-elimination by Gentzen. As a side note, we also give an
ultrafilter-based interpretation for intuitionism, formulating MRLJ as a
natural generalization of intuitionistic logic (IL). An immediate application
of LMRL can be found in a formulation of session types for channels that
support multiparty communication in distributed programming. We present a
multi-threaded lambda-calculus (MTLC) where threads communicate on linearly
typed multiparty channels that are directly rooted in LMRL, establishing for
MTLC both type preservation and global progress. The primary contribution of
the paper consists of both identifying multirole logic as a new form of logic
and establishing a theoretical foundation for it, and the secondary
contribution lies in applying multirole logic to the practical domain of
distributed programming.Comment: arXiv admin note: text overlap with arXiv:1604.0302
Towards compact bandwidth and efficient privacy-preserving computation
In traditional cryptographic applications, cryptographic mechanisms are employed to ensure the security and integrity of communication or storage. In these scenarios, the primary threat is usually an external adversary trying to intercept or tamper with the communication between two parties. On the other hand, in the context of privacy-preserving computation or secure computation, the cryptographic techniques are developed with a different goal in mind: to protect the privacy of the participants involved in a computation from each other. Specifically, privacy-preserving computation allows multiple parties to jointly compute a function without revealing their inputs and it has numerous applications in various fields, including finance, healthcare, and data analysis. It allows for collaboration and data sharing without compromising the privacy of sensitive data, which is becoming increasingly important in today's digital age. While privacy-preserving computation has gained significant attention in recent times due to its strong security and numerous potential applications, its efficiency remains its Achilles' heel. Privacy-preserving protocols require significantly higher computational overhead and bandwidth when compared to baseline (i.e., insecure) protocols. Therefore, finding ways to minimize the overhead, whether it be in terms of computation or communication, asymptotically or concretely, while maintaining security in a reasonable manner remains an exciting problem to work on. This thesis is centred around enhancing efficiency and reducing the costs of communication and computation for commonly used privacy-preserving primitives, including private set intersection, oblivious transfer, and stealth signatures. Our primary focus is on optimizing the performance of these primitives.Im Gegensatz zu traditionellen kryptografischen Aufgaben, bei denen Kryptografie verwendet wird, um die Sicherheit und Integrität von Kommunikation oder Speicherung zu gewährleisten und der Gegner typischerweise ein Außenstehender ist, der versucht, die Kommunikation zwischen Sender und Empfänger abzuhören, ist die Kryptografie, die in der datenschutzbewahrenden Berechnung (oder sicheren Berechnung) verwendet wird, darauf ausgelegt, die Privatsphäre der Teilnehmer voreinander zu schützen. Insbesondere ermöglicht die datenschutzbewahrende Berechnung es mehreren Parteien, gemeinsam eine Funktion zu berechnen, ohne ihre Eingaben zu offenbaren. Sie findet zahlreiche Anwendungen in verschiedenen Bereichen, einschließlich Finanzen, Gesundheitswesen und Datenanalyse. Sie ermöglicht eine Zusammenarbeit und Datenaustausch, ohne die Privatsphäre sensibler Daten zu kompromittieren, was in der heutigen digitalen Ära immer wichtiger wird. Obwohl datenschutzbewahrende Berechnung aufgrund ihrer starken Sicherheit und zahlreichen potenziellen Anwendungen in jüngster Zeit erhebliche Aufmerksamkeit erregt hat, bleibt ihre Effizienz ihre Achillesferse. Datenschutzbewahrende Protokolle erfordern deutlich höhere Rechenkosten und Kommunikationsbandbreite im Vergleich zu Baseline-Protokollen (d.h. unsicheren Protokollen). Daher bleibt es eine spannende Aufgabe, Möglichkeiten zu finden, um den Overhead zu minimieren (sei es in Bezug auf Rechen- oder Kommunikationsleistung, asymptotisch oder konkret), während die Sicherheit auf eine angemessene Weise gewährleistet bleibt. Diese Arbeit konzentriert sich auf die Verbesserung der Effizienz und Reduzierung der Kosten für Kommunikation und Berechnung für gängige datenschutzbewahrende Primitiven, einschließlich private Schnittmenge, vergesslicher Transfer und Stealth-Signaturen. Unser Hauptaugenmerk liegt auf der Optimierung der Leistung dieser Primitiven
An Infinite Needle in a Finite Haystack: Finding Infinite Counter-Models in Deductive Verification
First-order logic, and quantifiers in particular, are widely used in
deductive verification. Quantifiers are essential for describing systems with
unbounded domains, but prove difficult for automated solvers. Significant
effort has been dedicated to finding quantifier instantiations that establish
unsatisfiability, thus ensuring validity of a system's verification conditions.
However, in many cases the formulas are satisfiable: this is often the case in
intermediate steps of the verification process. For such cases, existing tools
are limited to finding finite models as counterexamples. Yet, some quantified
formulas are satisfiable but only have infinite models. Such infinite
counter-models are especially typical when first-order logic is used to
approximate inductive definitions such as linked lists or the natural numbers.
The inability of solvers to find infinite models makes them diverge in these
cases. In this paper, we tackle the problem of finding such infinite models.
These models allow the user to identify and fix bugs in the modeling of the
system and its properties. Our approach consists of three parts. First, we
introduce symbolic structures as a way to represent certain infinite models.
Second, we describe an effective model finding procedure that symbolically
explores a given family of symbolic structures. Finally, we identify a new
decidable fragment of first-order logic that extends and subsumes the
many-sorted variant of EPR, where satisfiable formulas always have a model
representable by a symbolic structure within a known family. We evaluate our
approach on examples from the domains of distributed consensus protocols and of
heap-manipulating programs. Our implementation quickly finds infinite
counter-models that demonstrate the source of verification failures in a simple
way, while SMT solvers and theorem provers such as Z3, cvc5, and Vampire
diverge
Revisiting the growth of polyregular functions: output languages, weighted automata and unary inputs
Polyregular functions are the class of string-to-string functions definable
by pebble transducers (an extension of finite automata) or equivalently by MSO
interpretations (a logical formalism). Their output length is bounded by a
polynomial in the input length: a function computed by a -pebble transducer
or by a -dimensional MSO interpretation has growth rate .
Boja\'nczyk has recently shown that the converse holds for MSO
interpretations, but not for pebble transducers. We give significantly
simplified proofs of those two results, extending the former to first-order
interpretations by reduction to an elementary property of -weighted
automata. For any , we also prove the stronger statement that there is some
quadratic polyregular function whose output language differs from that of any
-fold composition of macro tree transducers (and which therefore cannot be
computed by any -pebble transducer).
In the special case of unary input alphabets, we show that pebbles
suffice to compute polyregular functions of growth . This is obtained
as a corollary of a basis of simple word sequences whose ultimately periodic
combinations generate all polyregular functions with unary input. Finally, we
study polyregular and polyblind functions between unary alphabets (i.e. integer
sequences), as well as their first-order subclasses.Comment: 27 pages, not submitted ye
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