Disjunctive form and the modal μ\mu alternation hierarchy

This paper studies the relationship between disjunctive form, a syntactic normal form for the modal mu calculus, and the alternation hierarchy. First it shows that all disjunctive formulas which have equivalent tableau have the same syntactic alternation depth. However, tableau equivalence only preserves alternation depth for the disjunctive fragment: there are disjunctive formulas with arbitrarily high alternation depth that are tableau equivalent to alternation-free non-disjunctive formulas. Conversely, there are non-disjunctive formulas of arbitrarily high alternation depth that are tableau equivalent to disjunctive formulas without alternations. This answers negatively the so far open question of whether disjunctive form preserves alternation depth. The classes of formulas studied here illustrate a previously undocumented type of avoidable syntactic complexity which may contribute to our understanding of why deciding the alternation hierarchy is still an open problem.Comment: In Proceedings FICS 2015, arXiv:1509.0282

”KUN TULEE KRISIN OVESTA SISÄÄN, VOI LUOTTAA SIIHE, ET TYÖNTEKIJÖILLÄ ON OMA TAUSTA”- Satakuntalaisten kokemuksia KRIS Ry:n toiminnasta päihteettömyyden tukemisessa sekä ajatuksia toiminnan aloittamisesta Porissa

Opinnäytetyön tarkoituksena oli haastattelujen avulla kerätä tietoja KRIS ry:n toiminnasta päihteettömyyden tukemisessa haastattelemalla rikos- ja päihdetaustaisia entisiä satakuntalaisia, jotka ovat mukana KRISin toiminnassa. Lisäksi tarkoituksena oli selvittää, miksi haastateltavat ovat Satakunnasta pois lähteneet, sekä mitä he ajattelevat, jos KRIS saisi oman toimipaikan Poriin. Opinnäytetyön teoriaosuudessa tarkastellaan rikollisuutta ja päihteiden käyttöä tilastojen kautta sekä avataan lyhyesti syitä päihteiden käyttöön ja päihteiden yhteyttä rikolliseen toimintaan. Sakko, vankeus ja yhdyskuntaseuraamukset on kerrottu lyhyesti. Lisäksi esitellään päihderiippuvuus ja vertaistoiminta ja -tuki määritelminä, kerrotaan päihdehoidoista kunnissa lyhyesti sekä avataan KRIS ry:n toimintaa. Vertaistoiminta ja vertaistuki koettiin tärkeimmäksi asiaksi päihteettömyyden tukemisessa KRIS ry:n toiminnassa. Haastateltavat olivat sitä mieltä, että ilman KRIS ry:tä he tuskin olisivat päässeet irti päihteistä ja rikoskierteestä. Heistä oli myös helpompaa puhua ihmiselle, jolla itsellään on ollut samanlainen elämäntilanne joskus aiemmin. Satakunnasta haastateltavat olivat muuttaneet pois, koska koettiin, että Satakunnasta puuttuu ”toipumisen kulttuuri” ja päihteet sekä rikokset olisivat tulleet takaisin elä-mään kuntoutusjakson/vankilatuomion jälkeen. Muita syitä pois lähtemiseen olivat myös halu pysyä hengissä sekä traumaattiset kokemukset päihde-elämästä. KRIS ry:n toiminnan aloitus Porissa nähtiin positiivisena asiana, koska tarvetta tällaiselle toiminnalle on koko Satakunnassa. Yhteistyö eri toimijoiden välillä koettiin ensisijaisen tärkeäksi etenkin toiminnan alkaessa.The purpose of this thesis was to gather information of CRIS activities of support living without substances by interviewing former Satakunta peoples who has history of crimes and substances and who are involved in the CRIS activities. In addition, the purpose was to figure out why they left from Satakunta, as well as what they think, if CRIS could have own office in Pori. The theoretical part of the thesis examines crime and substances use through statistics, and briefly explains the reasons for the substance use and, consequently, criminal activity. Fines, imprisonment and community sanctions have been told briefly. In addition, it is presented drug addiction and peer activities and support set, describes briefly substance abuse treatment in the municipalities and opened the CRIS activities. Peer activities and peer support was the most important issue to support life without substances in CRIS`s activities. The interviewees thought that without the CRIS they would hardly have been able to get away from substances and criminal circles, and they thought also, that it was easier to talk to a person who has had a similar life situ-ation in the past. The interviewees had moved out of Satakunta, because it was felt, that Satakunta lacked a “culture of recovery” and the substances and crimes would have come back to life after rehabilitation period/jail sentence. Other reasons to move away was desir-ing to stay alive and the traumatic experiences of substance abuse-life. CRIS`s activities start in Pori was a positive thing, because this type of activity is needed in Satakunta. The co-operation between the different actors was perceived as a priority especially in the beginning of operation

Deciding the First Levels of the Modal mu Alternation Hierarchy by Formula Construction

We construct, for any sentence of the modal mu calculus Psi, derived sentences in the modal fragment and the fragment without least fixpoints of the modal mu calculus such that Psi is equivalent to a formula in these fragments if and only if it is equivalent to these formulas. The formula without greatest fixpoints that Psi is equivalent to if and only if it is equivalent to any formula without greatest fixpoint is obtained by duality. This yields a constructive proof of decidability of the first levels of the modal mu alternation hierarchy. The blow-up incurred by turning Psi into the modal formula is shown to be necessary: there are modal formulas that can be expressed sub-exponentially more efficiently with the use of fixpoints. For the fragments with only greatest or least fixpoints however, as long as formulas are in disjunctive form, the transformation into a formula syntactically in these fragments does not increase the size of the formula

Good for Games Automata: From Nondeterminism to Alternation

A word automaton recognizing a language $L$ is good for games (GFG) if its composition with any game with winning condition $L$ preserves the game's winner. While all deterministic automata are GFG, some nondeterministic automata are not. There are various other properties that are used in the literature for defining that a nondeterministic automaton is GFG, including "history-deterministic", "compliant with some letter game", "good for trees", and "good for composition with other automata". The equivalence of these properties has not been formally shown. We generalize all of these definitions to alternating automata and show their equivalence. We further show that alternating GFG automata are as expressive as deterministic automata with the same acceptance conditions and indices. We then show that alternating GFG automata over finite words, and weak automata over infinite words, are not more succinct than deterministic automata, and that determinizing B\"uchi and co-B\"uchi alternating GFG automata involves a $2^{\Theta(n)}$ state blow-up. We leave open the question of whether alternating GFG automata of stronger acceptance conditions allow for doubly-exponential succinctness compared to deterministic automata.Comment: Full version of a paper of the same name accepted fr publication at the 30th International Conference on Concurrency Theor

REGISTER GAMES

The complexity of parity games is a long standing open problem that saw a major breakthrough in 2017 when two quasi-polynomial algorithms were published. This article presents a third, independent approach to solving parity games in quasi-polynomial time, based on the notion of register game, a parameterised variant of a parity game. The analysis of register games leads to a quasi-polynomial algorithm for parity games, a polynomial algorithm for restricted classes of parity games and a novel measure of complexity, the register index, which aims to capture the combined complexity of the priority assignement and the underlying game graph. We further present a translation of alternating parity word automata into alternating weak automata with only a quasi-polynomial increase in size, based on register games; this improves on the previous exponential translation. We also use register games to investigate the parity index hierarchy: while for words the index hierarchy of alternating parity automata collapses to the weak level, and for trees it is strict, for structures between trees and words, it collapses logarithmically, in the sense that any parity tree automaton of size n is equivalent, on these particular classes of structures, to an automaton with a number of priorities logarithmic in n

Good-for-games ω\omega-Pushdown Automata

We introduce good-for-games $\omega$-pushdown automata ($\omega$-GFG-PDA). These are automata whose nondeterminism can be resolved based on the input processed so far. Good-for-gameness enables automata to be composed with games, trees, and other automata, applications which otherwise require deterministic automata. Our main results are that $\omega$-GFG-PDA are more expressive than deterministic $\omega$- pushdown automata and that solving infinite games with winning conditions specified by $\omega$-GFG-PDA is EXPTIME-complete. Thus, we have identified a new class of $\omega$-contextfree winning conditions for which solving games is decidable. It follows that the universality problem for $\omega$-GFG-PDA is in EXPTIME as well. Moreover, we study closure properties of the class of languages recognized by $\omega$-GFG- PDA and decidability of good-for-gameness of $\omega$-pushdown automata and languages. Finally, we compare $\omega$-GFG-PDA to $\omega$-visibly PDA, study the resources necessary to resolve the nondeterminism in $\omega$-GFG-PDA, and prove that the parity index hierarchy for $\omega$-GFG-PDA is infinite.Comment: Extended version of LICS'20 paper of the same name (DOI 10.1145/3373718.3394737); accepted for publication to LMC

History Determinism vs. Good for Gameness in Quantitative Automata

Automata models between determinism and nondeterminism/alternations can retain some of the algorithmic properties of deterministic automata while enjoying some of the expressiveness and succinctness of nondeterminism. We study three closely related such models - history determinism, good for gameness and determinisability by pruning - on quantitative automata. While in the Boolean setting, history determinism and good for gameness coincide, we show that this is no longer the case in the quantitative setting: good for gameness is broader than history determinism, and coincides with a relaxed version of it, defined with respect to thresholds. We further identify criteria in which history determinism, which is generally broader than determinisability by pruning, coincides with it, which we then apply to typical quantitative automata types. As a key application of good for games and history deterministic automata is synthesis, we clarify the relationship between the two notions and various quantitative synthesis problems. We show that good-for-games automata are central for "global" (classical) synthesis, while "local" (good-enough) synthesis reduces to deciding whether a nondeterministic automaton is history deterministic

An Analysis of Finnish Debtors Who Defaulted in 2014–2016 Because of Unsecured Credit Products

Consumer credit has become an important element of the economy despite the negative effects: Over-indebtedness has wide-ranging repercussions affecting consumers and society as a whole. We analysed the debt judgements (N= 4,095) of Finnish district courts from 2014 to 2016, as well as administrative data on debtors. Our focus was on the position of consumers on the credit market and their consumption-related problem debts, namely instant loans, extensive consumer credit, and credit-card as well as distance-selling indebtedness. Regarding the four credit products, first we considered the average amount of outstanding debt and then we looked at the sociodemographic and socioeconomic characteristics of the debtors. The results revealed that the average outstanding debt (E) varied according to the credit product and that the highest average amount originated from extensive consumer credit. Instant loans and distance-selling indebtedness caused debt problems especially among low-income young adults, adverse selection seemingly being one factor behind instant-loan-related debts. Extensive consumer credit and credit-card indebtedness were behind debt judgements against older consumers with a good socioeconomic position and numerous previous loans. This is a moral-hazard situation whereby borrowers may have more information about their total amounts of debt than the lenders. We suggest that, in many cases, debt problems reflect an abundant supply of consumer credit, which seems to foster asymmetric information, the consumer's position and competence to act in the credit market, as well as various overall risk factors. The findings highlight the need to strengthen consumers' financial skills and for loan products that meet the needs of low-credit-rated consumers. Moreover, lenders should act responsibly in the current credit market.Peer reviewe