701 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
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
Learning Possibilistic Logic Theories
Vi tar opp problemet med å lære tolkbare maskinlæringsmodeller fra usikker og manglende informasjon. Vi utvikler først en ny dyplæringsarkitektur, RIDDLE: Rule InDuction with Deep LEarning (regelinduksjon med dyp læring), basert på egenskapene til mulighetsteori. Med eksperimentelle resultater og sammenligning med FURIA, en eksisterende moderne metode for regelinduksjon, er RIDDLE en lovende regelinduksjonsalgoritme for å finne regler fra data. Deretter undersøker vi læringsoppgaven formelt ved å identifisere regler med konfidensgrad knyttet til dem i exact learning-modellen. Vi definerer formelt teoretiske rammer og viser forhold som må holde for å garantere at en læringsalgoritme vil identifisere reglene som holder i et domene. Til slutt utvikler vi en algoritme som lærer regler med tilhørende konfidensverdier i exact learning-modellen. Vi foreslår også en teknikk for å simulere spørringer i exact learning-modellen fra data. Eksperimenter viser oppmuntrende resultater for å lære et sett med regler som tilnærmer reglene som er kodet i data.We address the problem of learning interpretable machine learning models from uncertain and missing information. We first develop a novel deep learning architecture, named RIDDLE (Rule InDuction with Deep LEarning), based on properties of possibility theory. With experimental results and comparison with FURIA, a state of the art method, RIDDLE is a promising rule induction algorithm for finding rules from data. We then formally investigate the learning task of identifying rules with confidence degree associated to them in the exact learning model. We formally define theoretical frameworks and show conditions that must hold to guarantee that a learning algorithm will identify the rules that hold in a domain. Finally, we develop an algorithm that learns rules with associated confidence values in the exact learning model. We also propose a technique to simulate queries in the exact learning model from data. Experiments show encouraging results to learn a set of rules that approximate rules encoded in data.Doktorgradsavhandlin
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Quantitative Hennessy-Milner Theorems via Notions of Density
The classical Hennessy-Milner theorem is an important tool in the analysis of concurrent processes;
it guarantees that any two non-bisimilar states in finitely branching labelled transition systems can
be distinguished by a modal formula. Numerous variants of this theorem have since been established
for a wide range of logics and system types, including quantitative versions where lower bounds on
behavioural distance (e.g. in weighted, metric, or probabilistic transition systems) are witnessed
by quantitative modal formulas. Both the qualitative and the quantitative versions have been
accommodated within the framework of coalgebraic logic, with distances taking values in quantales,
subject to certain restrictions, such as being so-called value quantales. While previous quantitative
coalgebraic Hennessy-Milner theorems apply only to liftings of set functors to (pseudo)metric spaces,
in the present work we provide a quantitative coalgebraic Hennessy-Milner theorem that applies more
widely to functors native to metric spaces; notably, we thus cover, for the first time, the well-known
Hennessy-Milner theorem for continuous probabilistic transition systems, where transitions are given
by Borel measures on metric spaces, as an instance of such a general result. In the process, we also
relax the restrictions imposed on the quantale, and additionally parametrize the technical account
over notions of closure and, hence, density, providing associated variants of the Stone-Weierstraß
theorem; this allows us to cover, for instance, behavioural ultrametrics.publishe
Undergraduate and Graduate Course Descriptions, 2023 Spring
Wright State University undergraduate and graduate course descriptions from Spring 2023
Solving Odd-Fair Parity Games
This paper discusses the problem of efficiently solving parity games where
player Odd has to obey an additional 'strong transition fairness constraint' on
its vertices -- given that a player Odd vertex is visited infinitely often,
a particular subset of the outgoing edges (called live edges) of has to be
taken infinitely often. Such games, which we call 'Odd-fair parity games',
naturally arise from abstractions of cyber-physical systems for planning and
control.
In this paper, we present a new Zielonka-type algorithm for solving Odd-fair
parity games. This algorithm not only shares 'the same worst-case time
complexity' as Zielonka's algorithm for (normal) parity games but also
preserves the algorithmic advantage Zielonka's algorithm possesses over other
parity solvers with exponential time complexity.
We additionally introduce a formalization of Odd player winning strategies in
such games, which were unexplored previous to this work. This formalization
serves dual purposes: firstly, it enables us to prove our Zielonka-type
algorithm; secondly, it stands as a noteworthy contribution in its own right,
augmenting our understanding of additional fairness assumptions in two-player
games.Comment: To be published in FSTTCS 202
Quantitative Graded Semantics and Spectra of Behavioural Metrics
Behavioural metrics provide a quantitative refinement of classical two-valued
behavioural equivalences on systems with quantitative data, such as metric or
probabilistic transition systems. In analogy to the classical
linear-time/branching-time spectrum of two-valued behavioural equivalences on
transition systems, behavioural metrics come in various degrees of granularity,
depending on the observer's ability to interact with the system. Graded monads
have been shown to provide a unifying framework for spectra of behavioural
equivalences. Here, we transfer this principle to spectra of behavioural
metrics, working at a coalgebraic level of generality, that is, parametrically
in the system type. In the ensuing development of quantitative graded
semantics, we discuss presentations of graded monads on the category of metric
spaces in terms of graded quantitative equational theories. Moreover, we obtain
a canonical generic notion of invariant real-valued modal logic, and provide
criteria for such logics to be expressive in the sense that logical distance
coincides with the respective behavioural distance. We thus recover recent
expressiveness results for coalgebraic branching-time metrics and for trace
distance in metric transition systems; moreover, we obtain a new expressiveness
result for trace semantics of fuzzy transition systems. We also provide a
number of salient negative results. In particular, we show that trace distance
on probabilistic metric transition systems does not admit a characteristic
real-valued modal logic at all
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