Volume 2, Number 4 Published by the Association for Computing Machinery Special Interest Group on Logic and Computation October 2015 SIGLOG news TABLE OF CONTENTS General Information 1 From the Editor Andrzej Murawski 2 Chair's Letter Prakash Panangaden Technical Columns 3 Automata Mikołaj Bojańczyk 16 Verication Neha Rungta Announcements 26 Gödel Prize - Call for Nominations 28 SIGLOG Monthly 175 SIGLOG NEWS Published by the ACM Special Interest Group on Logic and Computation SIGLOG Executive Committee Chair Prakash Panangaden McGill University Vice-Chair Luke Ong University of Oxford Treasurer Natarajan Shankar SRI International Secretary Alexandra Silva Radboud University Nijmegen Catuscia Palamidessi INRIA and LIX, Ecole´ Polytechnique EACSL President Anuj Dawar University of Cambridge EATCS President Luca Aceto Reykjavik University ACM ToCL E-in-C Dale Miller INRIA and LIX, Ecole´ Polytechnique Andrzej Murawski University of Warwick Veronique´ Cortier CNRS and LORIA, Nancy ADVISORY BOARD Mart´ın Abadi Google and UC Santa Cruz Phokion Kolaitis University of California, Santa Cruz Dexter Kozen Cornell University Gordon Plotkin University of Edinburgh Moshe Vardi Rice University COLUMN EDITORS Automata Mikołaj Bojanczyk´ University of Warsaw Complexity Neil Immerman University of Massachusetts Amherst Security and Privacy Matteo Maffei CISPA, Saarland University Semantics Mike Mislove Tulane University Verification Neha Rungta SGT Inc. and NASA Ames Notice to Contributing Authors to SIG Newsletters By submitting your article for distribution in this Special Interest Group publication, you hereby grant to ACM the following non-exclusive, perpetual, worldwide rights: — to publish in print on condition of acceptance by the editor — to digitize and post your article in the electronic version of this publication — to include the article in the ACM Digital Library and in any Digital Library related services — to allow users to make a personal copy of the article for noncommercial, educational or research purposes However, as a contributing author, you retain copyright to your article and ACM will refer requests for republication directly to you. SIGLOG News (ISSN 2372-3491) is an electronic quarterly publication by the Associa- tion for Computing Machinery. From the Editor Welcome to another issue of SIGLOG News! In this issue – SIGLOG’s Chair Prakash Panangaden announces an election and reports on the out- come of a recent meeting of the SIG Governing Board. – Mikołaj Bojanczyk´ investigates boundedness in the Automata Column. – Darren Cofer writes about certifying avionics software in Neha Rungta’s column on Verification. – And, as usual, there are numerous calls for papers and participation in our monthly bulletin, prepared by Daniela Petris¸an. SIGLOG News is still looking for more volunteers for coordinating sections on confe- rence reports and book reviews. Please email [email protected] if you are interested. Enjoy! Andrzej Murawski University of Warwick SIGLOG News Editor ACM SIGLOG News 1 October 2015, Vol. 2, No. 4 Chair’s Letter First, a major piece of good news. The SIG Governing Board of ACM has approved SIGLOG and moved us out of the probationary status that we were in. Every four years a SIG is subjected to a viability review. As we were just started in 2014 we were assessed in 18 months and passed with flying colours. Congratulations to the members for making SIGLOG a flourishing organization. We will be evaluated again in two years, instead of the usual four, because we are still in the start up phase. Election fever is upon us! No, I am not referring to the US Presidential election nor the Canadian Federal election but to the election of new office holders for SIGLOG along with members-at-large to serve on the executive committee. The chair of the nominating committee is Dale Miller, who will ensure that we have a full slate of can- didates by December. In January the candidates will publish their vision statements in the SIGLOG Newsletter and the elections will take place in 2016. Any professional member of the ACM who is a member of SIGLOG can run for office. Please do contact Dale (before he twists your arm!) if you would like to run in the election. Prakash Panangaden McGill University ACM SIGLOG Chair ACM SIGLOG News 2 October 2015, Vol. 2, No. 4 AUT AUTOMATA COLUMN MIKOŁAJ BOJANCZYK´ , University of Warsaw [email protected] U MIKOŁAJ BOJANCZYK,´ University of Warsaw This is a survey of extensions of logics and automata which talk about boundedness. A typical property of interest is the set of !-words which satisfy “there exists some k, such that every a letter is followed by a b letter in at most k steps”. The main points of interest are the logic MSO+U, its fragments and related automata models, as well as the regular cost functions of Colcombet. To begin our discussion of boundedness, consider one of the archetypical liveness properties, namely “every a event is followed by a b event in a finite number steps”. In the syntax of linear temporal logic LTL, this property is written as G a Fb . ) What could be more natural than asking for the b to appear in a bounded number of steps? Adding such boundedness constraints is the idea behind prompt LTL, a logic introduced in [Kupferman et al. 2009]. In prompt LTL, one writes formulas like k k N G a F b , 9 2 ) k where F means “in at most k steps”. Assuming that we are talking about languages of !-words over the alphabet a, b , the language that corresponds to the above formula { } of prompt LTL is an1 ban2 ban3 b :limsupn < . { ··· i 1} This language will be our running example. The goal of this paper is to discuss logics and automata which describe the running example and its variants. There are three sources of motivation. A richer modelling language. The first source of motivation, highlighted by the prompt LTL example, is that boundedness is one of the most basic kinds of asymptotic properties, and it is therefore unsurprising that it has found its way into formalisms expressing properties of infinite computation. For example, one can consider variants of parity games (and Streett, etc.) where the winning condition requires that some- thing good happens in a bounded amount of time [Chatterjee et al. 2009; Bloem et al. 2009; Fijalkow and Zimmermann 2014]. A new tool in a logician’s toolbox. The second source motivation is that boundedness questions appear implicitly when solving problems without an explicit boundedness character. A famous example is the star height problem. As discovered by Hashigu- chi [Hashiguchi 1988], this problem can be solved by reducing it to a decidable boun- ACM SIGLOG News 3 October 2015, Vol. 2, No. 4 dedness problem, to be discussed later in this paper. Other problems in formal lan- guage theory that reduce to boundedness questions include the star height problem for regular tree languages [Colcombet and Loding¨ 2008a], or the Mostowski index pro- blem for automata on infinite trees [Colcombet and Loding¨ 2008b], although in the latter case, both the Mostowski index problem and its corresponding boundedness pro- blem remain open, see [Fijalkow et al. 2015] for recent developments. Another example of a problem that reduces to a boundedness question is the finite satisfiability problem for fixpoint logics such as: the modal µ-calculus with backward modalities [Bojanczyk´ 2002], guarded fixpoint logic [Bar´ any´ and Bojanczyk´ 2012] or guarded negation lo- gic [Bar´ any´ et al. 2015]. Other examples where boundedness questions arise include: a question about eliminating fixpoint operators in [Blumensath et al. 2014c], a satis- fiability question for a variant of CTL* in [Carapelle et al. 2013], or a characterisation of behaviours of communicating timed automata [Aminof et al. 2015]. Understanding regularity. A third source of motivation is the quest for understan- ding “regular languages” for infinite objects, such as !-words. Consider the language in the running example. Is it a “regular language”? It is not regular in the accepted sense, i.e. it is not recognised by any nondeterministic Buchi¨ automaton (a straightforward pumping argument), and therefore it is also not definable by any formula of monadic second-order logic MSO. Nevertheless, the language looks innocent enough, and one may wonder whether it might belong to some class of languages with a simple defini- tion, maybe of a logical character, and with good closure and decidability properties. The main topic of this paper is to survey several proposals for such classes. Counting without actually counting. The motivation of “understanding regularity” also limits the scope of logics studied in this paper. We would like the languages to resemble “regular” languages in some way. For example, for languages of !-words, at the very least we require every language L A! to have finitely many equivalence ✓ classes for the Myhill-Nerode equivalence relation on finite words w, v A⇤ defined by 2 w v if u A! wu L vu L. ⇠L 8 2 2 () 2 Such a restriction means that any counting can only be done in some asymptotic way. This excludes all sort of boundedness questions where precise counting is involved, e.g. the rich body of literature on boundedness for vector addition systems. 1. AUTOMATA WITH COUNTERS To the author’s knowledge, the first deeper study of boundedness in automata and logic was in the context of the star height problem. We begin our story with these automata. 1.1. Automata for star height Distance automata. A distance automaton is the same as a nondeterministic auto- maton over finite words, except that it has a distinguished subset of transitions, which are assumed to be “costly”. Another view on distance automata, which will be used in this paper, is that a distance automaton is a very restricted kind of counter automa- ton, which has a single counter that is incremented whenever a costly transition is encountered.