Seventh NII Type Theory Workshop
Date: February 6, 2012, 13:00--17:00
Place: National Institute of Informatics, Room 2005 (20th floor)
場所: 国立情報学研究所 20階 2005室
(半蔵門線,都営地下鉄三田線・新宿線 神保町駅または東西線 竹橋駅より徒歩5分)
(地図 http://www.nii.ac.jp/introduce/access1-j.shtml)
Program:
13:00--13:30 Daisuke Kimura (National Institute of Informatics)
Title: A generalized modal lambda calculus
13:30--14:00 Kazuyuki Asada (National Institute of Informatics)
Title: Semantics of Multi-rooted Graph with Ordered Branch
14:00--14:20 Tea Break
14:20--15:00 Makoto Tatsuta (National Institute of Informatics)
Title: Type Inference for Bimorphic Recursion
15:00--15:40 Yukiyoshi Kameyama (University of Tsukuba)
Title: Pseudo-Classical Modal Logic for Staged Computation
15:40--16:00 Tea Break
16:00--17:00 Stefano Berardi (Torino University)
Title: A Game Semantic for various Subclassical Logics
Abstracts:
----------------------------------------------------------------------
Daisuke Kimura (National Institute of Informatics)
Title: A generalized modal lambda calculus
Abstract: In this talk, we introduce a lambda calculus with modal
types. The types of this system contain information of possible worlds
explicitly. This information can be considered as a position which is
an abstraction of time or place. The feature of our calculus is that
we can change the property of modalities by changing information about
the relationship between positions. The aim of our research is the
following: (1) To clarify the computational meaning of necessity and
possibility modal operators. (2) To give a uniform framework that can
treat several calculi with modal types.
----------------------------------------------------------------------
Kazuyuki Asada (National Institute of Informatics)
Title: Semantics of Multi-rooted Graph with Ordered Branch
Abstract: Buneman et al. introduced a graph transformation language
UnCAL, where graph has bisimilarity semantics. There structural
recursion plays an important role, and in order to define it, they
introduced multi-rooted graph and its algebraic representation. In
this talk we give coalgebraic semantics for multi-rooted graph, and
see that such final coalgebras has some call-by-value structure. Then
we introduce a CBV equational theory. Next we modify the results of
graph with un-ordered branch to that with ordered branch, which is
important for application to XML. For this ordered graphs,
bisimilarity is defined in some subtle way, but we can use the ordered
version of above CBV equational theory for reasoning of the
bisimilarity between ordered graphs.
----------------------------------------------------------------------
Makoto Tatsuta (National Institute of Informatics)
Title: Type Inference for Bimorphic Recursion
Abstract: This talk proposes bimorphic recursion, which is restricted
polymorphic recursion such that every recursive call in the body of a
function definition has the same type. Bimorphic recursion allows us
to assign two different types to a recursively defined function: one
is for its recursive calls and the other is for its calls outside its
definition. Bimorphic recursion in this talk can be nested. This
talk shows bimorphic recursion has principal types and decidable type
inference. Hence bimorphic recursion gives us flexible typing for
recursion with decidable type inference. This talk also shows that
its typability becomes undecidable because of nesting of recursions
when one removes the instantiation property from the bimorphic
recursion. This is a joint work with Ferruccio Damiani.
----------------------------------------------------------------------
Yukiyoshi Kameyama (University of Tsukuba)
Title: Pseudo-Classical Modal Logic for Staged Computation
Abstract: In this talk, we study a pseudo-classical modal logic, which
corresponds to the staged calculus with control operators introduced
by our earlier work. Staged computation is a means for run-time code
generation, and has been proved useful in improving efficiency and
maintainability of software. We are interested in the use of control
operators in staged computation, since they play an essential role to
avoid the code duplication problem. Combining a staged calculus with
control operators in a naive way results in an unsound calculus, and
we need a restriction on the typing rule for lambda. We show that
this restriction has a logical counterpart similar to Nakano's
catch/throw calculus.
----------------------------------------------------------------------
Stefano Berardi (Torino University)
Title: A Game Semantic for various Subclassical Logics
Abstract: In this talk we describe the state of the art of game
semantics for Logic and lambda-calculus, and the motivations for
having a game semantics. Then we define a game semantic for
Intuitionism extending both Coquands and Hyland-Ongs game
semantics. The semantics refines a paper of TLCA 2007. We have two
kind of results: (1) (Soundness and Completeness) The recursive
winning strategy of our game semantics are isomorphic to the cut-free
proofs of some variant of HA-omega (Infinitary Intuitionistic
Arithmetic) (2) (Cut Elimination) Any debate between two terminating
strategies terminates. This is an ongoing joint work with M. Tatsuta.
----------------------------------------------------------------------
連絡先
龍田 真 (国立情報学研究所)
みなさま,
ETAPS 2012 附設ワークショップ
MATHEMATICALLY STRUCTURED FUNCTIONAL PROGRAMMING
のご案内です.
ワークショップですが,歴史を持つトピックだけあり,選りすぐりで
かっちりした論文が揃っています.
せっかくタリンにおいでならば,ぜひご出席ください!
蓮尾 一郎 (東大情報理工)
https://www-mmm.is.s.u-tokyo.ac.jp/~ichiro/
---------- Forwarded message ----------
From: Paul Levy <P.B.Levy(a)cs.bham.ac.uk>
Date: Thu, Jan 26, 2012 at 11:38 PM
Subject: categories: MSFP 2012 call for participation
To: categories list <categories(a)mta.ca>
Please note the deadline for early registration, including discounted
hotel bookings:
*Sunday 29 January*
===========================
Fourth Workshop on
MATHEMATICALLY STRUCTURED FUNCTIONAL PROGRAMMING
25 March, Tallinn, Estonia
A satellite workshop of ETAPS 2012
http://cs.ioc.ee/msfp/msfp2012/
The fourth workshop on Mathematically Structured Functional
Programming is devoted to the derivation of functionality from
structure. It is a celebration of the direct impact of Theoretical
Computer Science on programs as we write them today. Modern
programming languages, and in particular functional languages, support
the direct expression of mathematical structures, equipping
programmers with tools of remarkable power and abstraction. Where
would Haskell be without monads? Functional reactive programming
without arrows? Call-by-push-value without adjunctions? Type theory
without universes? The list goes on. This workshop is a forum for
researchers who seek to reflect mathematical phenomena in data and
control.
The first MSFP workshop was held in Kuressaare, Estonia, in July 2006,
affiliated with MPC 2006 and AMAST 2006. The second MSFP workshop was
held in Reykjavik, Iceland as part of ICALP 2008. The third MSFP
workshop was held in Baltimore, USA, as part of ICFP 2010.
Invited Talks:
=================
Dependently typed continuation monads as models in Logic
Danko Ilik, Goce Delčev University of Štip, Republic of Macedonia
Fibred Data Types
Neil Ghani, University of Strathclyde, UK
Accepted Papers
==================
• A Formal Comparison of Approaches to Datatype-Generic Programming
José Pedro Magalhães and Andres Löh
• An Investigation of the Laws of Traversals
Mauro Jaskelioff and Ondrej Rypacek
• Evaluation strategies for monadic computations
Tomas Petricek
• From Mathematics to Abstract Machine: A formal derivation of an
executable Krivine machine
Wouter Swierstra
• Irrelevance, Heterogenous Equality, and Call-by-value Dependent Type Systems
Vilhelm Sjöberg, Chris Casinghino, Ki Yung Ahn, Nathan Collins, Harley
D. Eades III, Peng Fu, Garrin Kimmell, Tim Sheard, Aaron Stump and
Stephanie Weirich
• Parametric Compositional Data Types
Tom Hvitved and Patrick Bahr
• Step-Indexed Normalization for a Language with General Recursion
Chris Casinghino, Vilhelm Sjöberg and Stephanie Weirich
• Tracing monadic computations and representing effects
Maciej Piróg and Jeremy Gibbons
ETAPS:
======
European Joint Conferences on Theory and Practice of Software (ETAPS)
is the primary European forum for academic and industrial researchers
working on topics relating to software science. ETAPS, established in
1998, is a confederation of six main annual conferences (one of them,
POST, being new in 2012), accompanied by satellite workshops. ETAPS
2012 is the fifteenth event in the series.
http://www.etaps.org/2012
Host City:
==========
Tallinn, a city of 412,000 people, is the capital and largest city of
Estonia, a small EU member country in Northern Europe, bordering
Russia to the East and Latvia to the south. Located in the north of
the country, on the southern shores of the Gulf of Finland, opposite
Helsinki in Finland, Tallinn is most well known for its picturesque
medieval Old Town, a UNESCO World Heritage site. But it also has a
vivid cultural scene, outperforming most European centres of similar
size. In 2011, Tallinn, along with Turku in Finland, is the Cultural
Capital of Europe.
Tallinn is easy to travel to. Estonia is part of Schengen and the
Eurozone. The Lennart Meri International Airport of Tallinn /TLL) is
only 4km from the city centre.
Programme Committee:
====================
* James Chapman (co-chair), Institute of Cybernetics, Tallinn, Estonia
* Paul Blain Levy (co-chair), University of Birmingham, UK
* Thorsten Altenkirch, University of Nottingham, UK
* Robert Atkey, University of Strathclyde, Glasgow, UK
* Nils Anders Danielsson, Chalmers University and University of Gothenburg,
Sweden
* Martin Escardo, University of Birmingham, UK
* Ichiro Hasuo, University of Tokyo, Japan
* Ralf Hinze, University of Oxford, UK
* Neelakantan Krishnaswami, Microsoft Research, Cambridge, UK
* Daniel R. Licata, Carnegie Mellon University, Pittsburgh, PA
* Ulrich Schoepp, LMU Munich, Germany
* Alex Simpson, University of Edinburgh, UK
* Matthieu Sozeau, INRIA, Paris, France
* Sam Staton, University of Cambridge, UK
Further Information:
====================
For more information about the workshop, go to:
http://cs.ioc.ee/msfp/msfp2012/
With any other questions please do not hesitate to contact the
co-chairs at msfp2012(a)easychair.org.
------------------------------------------------------------------
The International Interdisciplinary Conference
Philosophy, Mathematics, Linguistics: Aspects of Interaction 2012
(PhML 2012)
St. Petersburg, Russia, May 22-25, 2012
http://www.pdmi.ras.ru/EIMI/2012/PhML/index.htm
------------------------------------------------------------------
AIM and SCOPE
=============
The PhML 2012 is a sequel in the series of conferences
"Philosophy, Mathematics, Linguistics: Aspects of Interaction"
intended to provide a forum for presentation of current
researches, and to stimulate a dialogue between mathematicians,
logicians, philosophers, linguists and computer scientists who
share an interest in cross-disciplinary research. The conference
will have plenary sessions to present the latest researches. In
addition to plenary sessions, the conference will feature a panel
discussion entitled "The Heritage of Kant and Contemporary Formal
Logic". Apart from plenary sessions, there will also be parallel
sessions of thematic sections to present contributed papers.
The PhML 2012 will be held on May 22$BK(J5, 2012, at the Euler
International Mathematical Institute (EIMI), which is a part of
the St. Petersburg Department of Steklov Mathematical Institute
(PDMI).
PLENARY SPEAKERS
================
Theodora Achourioti (University of Amsterdam, the Netherlands)
Michel De Glas (CNRS - University Paris$BK%(Jiderot, France)
Dmitry Grigoriev (CNRS - University Lille 1, France)
Gerhard Heinzmann (Archives Henri-Poincare (UMR 7117)
University of Lorraine/CNRS, France)
Jaakko Hintikka (Boston University, USA)
Edward Karavaev (St. Petersburg State University, Russia)
Michiel van Lambalgen (University of Amsterdam, the Netherlands)
Yuri Manin (Max Planck Institute for Mathematics, Germany)- to be
confirmed
Grigori Mints (Stanford University, USA)
Andrey Patkul (St. Petersburg State University, Russia)
Jeff Pelletier (University of Alberta, Canada)
Graham Priest (City University of New York, USA,
University of Melbourne, Australia)
Oleg Prosorov (PDMI, St. Petersburg, Russia)
Andrei Rodin (University Paris$BK%(Jiderot, France)
Gabriel Sandu (University of Helsinki, Finland)
Anatol Slissenko (University Paris$BK&(Jst Cr$BqU(Jeil, LACL, France)
CALL for PAPERS
===============
The PhML 2012 invites to submit papers relating to the interplay
between philosophy, mathematics and linguistics for presentation
at thematic sections. Each presentation of a contributed paper
will be allotted 25 min, including 5 min for discussion.
Presentations should be given in English. Papers from any
tradition and from a wide variety of perspectives are welcome,
including but in no way limited to the following topics:
- New trends in the foundations of mathematics today;
- Ontology of mathematics and the nature of mathematical truth;
- The problem of abstract entities in mathematics, philosophy and
linguistics;
- Formalization of Kant's logic and theory of judgments;
- The mathematical concept of a function: from the notions of
mapping, transformation towards the notion of an algorithm;
- Complexity of finite objects: limited possibilities of man and
computer;
- Novel computational models and paradigms;
- Philosophical and mathematical aspects of informatics;
- Philosophical aspects of the use of natural language in
mathematics;
- Mathematical investigation of natural language structures;
- Mathematical models in the study of language.
PAPER SUBMISSION
================
Papers should be prepared in LaTeX or MS Word using style files of
PhML format and be submitted electronically as pdf and source
files via e-mail:
PhML_2012(a)pdmi.ras.ru
IMPORTANT DATES:
================
- Submission deadline for contributed papers: March 1st, 2012
- Notification of acceptance: March 15th, 2012
- Final date for camera-ready copy: April 22nd, 2012
- Conference: May 22-25, 2012
- Panel discussion: May 23, 2012
PROCEEDINGS
===========
The proceedings of PhML 2012 will be published by PDMI in the
local series with ISBN no.
ORGANIZING / PROGRAM COMMITTEE
==============================
Edward Karavaev (St. Petersburg State University, Russia),
Elena Lisanyuk (St. Petersburg State University, Russia),
Ivan Mikirtumov (St. Petersburg State University, Russia),
Yuri Nechitajlov (St. Petersburg State University, Russia),
Vladimir Orevkov (PDMI, St. Petersburg, Russia), co-chair,
Oleg Prosorov (PDMI, St. Petersburg, Russia), co-chair,
Anatol Slissenko (University Paris$BK&(Jst Cr$BqU(Jeil, LACL, France).
PARTICIPATION
=============
For registration and further practical information, see:
http://www.pdmi.ras.ru/EIMI/2012/PhML/index.htm
みなさま
今週木曜日に催されるセミナーのご案内をさせていただきます。
どうぞお気軽にお越しください。
照井
---
RIMS-CS website
http://www.kurims.kyoto-u.ac.jp/~cs/
=====
Speaker:
Stefano Berardi (University of Torino)
Title:
A Topology over a set of Knowledge States and a Fixed Point Problem
Date:
11.00 -, February 2nd (Thu)
Place:
Room 478, "Research Bldg. No. 2 (Sougou Kenkyu 2-Goukan)"
http://www.kyoto-u.ac.jp/en/access/campus/main.htm
(Next to our CS Lab)
総合研究2号館 478号室 (CS室のとなりです)
http://www.kyoto-u.ac.jp/ja/access/campus/map6r_y.htm
Abstract:
We give an abstract formulation of the termination problem
for realizer of Heyting Arithmetic plus various subsystem of classical
logic. This termination problem is expressed as the existence of a
fixed point for a class of continuous maps in a suitable topology.
------------------------------------------
Kazushige TERUI
Research Institute for Mathematical Sciences,
Kyoto University.
Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, JAPAN.
Phone: +81-75-753-7235
Fax: +81-75-753-7276
terui(a)kurims.kyoto-u.ac.jp
http://www.kurims.kyoto-u.ac.jp/~terui/
logic-mlの皆様,
量子情報のポスドク募集に関する代理投稿を
させていただきます.
大阪府立大学理学系研究科
西村治道
-------------------------------------------------------------------------------
立命館の山下茂と申します.
Masaryk University, Brno, Czech Republik での以下のポスドクの募集案内を日本
国内の量子情報関連MLへの配布を依頼されましたので、MLへ通して下記の案内
をさせてください。複数お受け取りになったらご容赦ください。
Postdoc position in Quantum Information at Faculty of Informatics,
Masaryk University, Brno, Czech Republik
A 2-year (with possible extension to 3 years) postdoctoral position in
Quantum
Information Processing Theory is opening in Faculty of Informatics, Masaryk
University, starting with September 2012, in the group of prof. Jozef
Gruska
(http://www.fi.muni.cz/quantum).
Possible research areas includes - but are not restricted to - models of
quantum computations, quantum algorithms, quantum cryptography, quantum
entanglement, quantum (pseudo-telepathic) games.
The successful candidate will be member of the Quantum information
processing
and cryptography laboratory that has currently 8 members including two
postdocs.
The group has close and intensive contacts with quantum groups in Bratislava
and Vienna,
Faculty of Informatics has more than 2500 students (http://www.fi.muni.cz)
and close contacts with Departments of mathematics and Physics of the
Faculty
of Natural sciences.
Applicants must hold a PhD - or be about to obtain one - in informatics,
physics or mathematics and should be able to demonstrate very good English
and strong research track record.
Once application is successful, position should be taken during the period
August 15 - September 1, 2012.
The following information should be provided in an application:
* CV
* PhD diploma
* A proof of good English (outcomes of TOEFL, CAE or an equivalent test).
* Statement of research interest
* Lists of publications and presentations
* Two representative publications
* Two letters of recommendations
Electronic publications are preferred. They should be sent via email to
gruska(a)fi.muni.cz or via postal mail to
Prof. Jozef Gruska
Faculty of Informatics
Masaryk University
Botanicka 68a
60200 Brno, Czech Republic
For the official web side of the whole postdocs programs and conditions
see http://www.mu.cz/research/postdoctoral
`
An applicant will receive 55000 Kc per month (what corresponds concerning
exchange rate to about 2200 EUR (and with respect to the living costs to
about
3000-3300 EUR in Western Europe). In addition, he/she will receive standard
health care insurance for himself/herself) Reasonable traveling and
office money are also available
皆様、こんにちは!
産総研の北村崇師です。
下記の通り、産総研組み込みシステム技術連携体(@尼崎)は、計算機言語談話
会 (CLC:Computer Language Colloquium)を開催します。
どなたでも無料で参加できます。皆様のご参加お待ちしております。
また参加の際は、事前に北村( t.kitamura(a)aist.go.jp )までメールによるご
連絡をお願いいたします。
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
日時:平成 24 年 2 月 1 日(水) 16:00--17: 30
場所:(独)産総研関西センター尼崎事業所 E 棟 2 階 セミナー室
http://cfv.jp/cvs/access/index.html
演題:Automatic Specification-Based Program Testing
講演者:Prof. Shaoying Liu (Hosei University, Tokyo, Japan)
梗概:
Automatic specification-based testing (ASBT) is a potentially effective
and efficient technique for detecting errors in programs and attractive
to industry due to its potential in saving time and cost. In this talk,
after presenting the goals of the testing technique I will introduce a
decompositional functional scenario-based testing technique, a specific
ASBT, by explaining the strategy and criteria for test set generation,
test oracle for test result analysis, and test process for tool support.
I will also discuss the challenges and future research directions.
Bio.:
Shaoying Liu is Professor at Hosei University, Japan. He received a Ph.D
in Computer Science from the University of Manchester, U.K in 1992. His
research interests include Formal Engineering Methods,
Specification-based Inspection and Testing, and Intelligent Software
Engineering Environments. He has published a book titled "Formal
Engineering for Industrial Software Development" with Springer-Verlag,
four edited conference proceedings, and over 120 academic papers in
refereed journals and international conferences. He is the chair of
Steering Committee for ICFEM conference, and on the editorial board for
the Journal of Software Testing, Verification and Reliability (STVR) and
for ISRN Software Engineering Journal. He is a Fellow of British
Computer Society, Senior member of IEEE Computer Society, and member of
Japan Society for Software Science and Technology.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
以上よろしくお願いいたします。
--------------------------
北村崇師 PhD <t.kitamura(a)aist.go.jp>
特別研究員
(独)産業技術総合研究所
組込みシステム技術連携研究体
〒661-0974 兵庫県尼崎市若王寺3-11-46
Tel: 06-6494-8054
Fax: 06-6494-8073
みなさま
1月31日(火)と2月9日(木)にJAISTで行われます、計算量・組合せ理論についての
2つセミナーをご案内致します。どうぞお気軽にお越しください。
http://www.jaist.ac.jp/is/labs/ogawa-lab/vs12.html
廣川
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Seminars of Research Center for Software Verification, JAIST
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
== Seminar I ==
Date: 31st Jan (Tue) 13:00-17:00 (closing time is flexible)
Place: JAIST IS school collaboration room 7 (5F)
1. Prof.Yijia Chen (Shanghai Jiao Tong University)
"Parameterized complexity of SAT"
Many natural computational problems are NP-hard, hence they have no
polynomial time algorithms assuming NP \ne P. The traditional
approaches for coping with such problems are heuristic and
approximation algorithms. Nevertheless, the heuristic algorithms
often lack a rigorous analysis, while the approximation algorithms
cannot guarantee exact solutions. Parameterized algorithms offer
another approach which achieves both criteria. The key observation
is that many natural problem instances come with some parameters
which can be expected to be small, e.g., the size of a vertex
cover, the length of a database query, and the tree width of a
graph. If an exponential time algorithm has its superpolynomial
behavior restricted by the parameters, it might well be efficient
in practice. As an example, there is an algorithm for SAT which is
exponential in the tree width tw(\alpha) of a given instance \alpha
and at the same time linear in the size of \alpha. Therefore, if
there is a constant upper bound on tw(\alpha), we can solve the
corresponding SAT in linear time.
In this talk I will survey some major tools for designing
parameterized algorithms, including bounded search tree,
kernelization, tree width method, and algorithmic meta-theorems,
etc, with a focus on applications to SAT. In passing, I will also
discuss some corresponding lower bound results.
2. Dr. Yohji Akama (Tohoku University)
"A new order theory of set systems, WQO and BQO"
A set system over a set $T$, a subfamily of the power set $P(T)$,
is a topic of (extremal) combinatorics, as well as a target of an
algorithm to learn in computational learning theory of languages.
A well quasi-ordering (WQO for short) is introduced by Higman and
employed in algebra, combinatorics, formal language theory, and so
on. A better quasi-ordering (BQO for short) is introduced by
Nash-Williams and employed in infinitary combinatorics and
verification of infinite-state systems.
We generalize WQOs and BQOs by using set systems, define the order
type of a set system from game-theoretic viewpoint and study
nondeterministic, combinatorial operations on set systems, such as
monotone (continuous) image and unbounded unions of set systems.
The motivating examples are the union of two colored arithmetical
progressions, and the discolorization, and new useful examples are
shuffle-product and shuffle-closure from formal language theory
Furthermore, we provide a neat correspondence :
quasi-orderings vs finitely branching simulations, and
set systems vs linear, monotone, continuous functions.
Next, we introduce a set system that has order type and corresponds
to a BQO. We prove that the class of set systems corresponding to
BQOs is closed by any monotone function. In (Shinohara and
Arimura. ``Inductive inference of unbounded unions of pattern
languages from positive data.'', Theoretical Computer Science,
pp.191-209, 2000), for any set system $L$, they considered the class
of arbitrary (finite) unions of members of $L$. From viewpoint of
WQOs and BQOs, we characterize the set systems $L$ such that the
class of arbitrary (finite) unions of members of $L$ has order type.
== Seminar II ==
Date: 9th Feb (Thu) 13:00-15:00 (closing time is flexible)
Place: JAIST IS school collaboration room 7 (5F)
* Prof.Yijia Chen (Shanghai Jiao Tong University)
"A Logic for PTIME and a Parameterized Halting Problem"
Whether there is a logic for polynomial time (PTIME) is the central
problem in finite model theory. When formalizing this problem,
Gurevich (1988), together with Blass, actually proposed a logic
LFP_inv, which is a version of least fixed-point logic plus some
additional invariance condition. Although they don't believe that
LFP_inv captures PTIME, no proof was given. Later, in a work of
Nash, Remmel, and Vianu (2005), it was shown that whether LFP_inv
captures PTIME is equivalent to the parameterized complexity of a
halting problem:
input: A nondeterministic Turing machine M and a natural number n
in unary.
parameter: |M|, i.e., the size of M
question: does M accept the empty input in at most n steps?
Our recent work (2010-11) reveals that it is even equivalent to an
open problem in proof complexity, i.e., whether there is a
polynomial optimal proof system for the set TAUT of tautologies of
propositional logic.
In this talk, I will discuss all these equivalences and their
extensions to some other complexity classes beside PTIME. It turns
out that Levin's optimal inverters (1973) play a central role in
the proofs.
This is joint work with Joerg Flum.