242 research outputs found
Synthesis of Deterministic Top-down Tree Transducers from Automatic Tree Relations
We consider the synthesis of deterministic tree transducers from automaton
definable specifications, given as binary relations, over finite trees. We
consider the case of specifications that are deterministic top-down tree
automatic, meaning the specification is recognizable by a deterministic
top-down tree automaton that reads the two given trees synchronously in
parallel. In this setting we study tree transducers that are allowed to have
either bounded delay or arbitrary delay. Delay is caused whenever the
transducer reads a symbol from the input tree but does not produce output. We
provide decision procedures for both bounded and arbitrary delay that yield
deterministic top-down tree transducers which realize the specification for
valid input trees. Similar to the case of relations over words, we use
two-player games to obtain our results.Comment: In Proceedings GandALF 2014, arXiv:1408.556
Bisimulations and Logical Characterizations on Continuous-time Markov Decision Processes
In this paper we study strong and weak bisimulation equivalences for
continuous-time Markov decision processes (CTMDPs) and the logical
characterizations of these relations with respect to the continuous-time
stochastic logic (CSL). For strong bisimulation, it is well known that it is
strictly finer than CSL equivalence. In this paper we propose strong and weak
bisimulations for CTMDPs and show that for a subclass of CTMDPs, strong and
weak bisimulations are both sound and complete with respect to the equivalences
induced by CSL and the sub-logic of CSL without next operator respectively. We
then consider a standard extension of CSL, and show that it and its sub-logic
without X can be fully characterized by strong and weak bisimulations
respectively over arbitrary CTMDPs.Comment: The conference version of this paper was published at VMCAI 201
A tool for model-checking Markov chains
Markov chains are widely used in the context of the performance and reliability modeling of various systems. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both discrete [34, 10] and continuous time settings [7, 12]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen-Twente Markov Chain Checker EĂMC2, where properties are expressed in appropriate extensions of CTL. We illustrate the general benefits of this approach and discuss the structure of the tool. Furthermore, we report on successful applications of the tool to some examples, highlighting lessons learned during the development and application of EĂMC2
Uniformization Problems for Synchronizations of Automatic Relations on Words
A uniformization of a binary relation is a function that is contained in the relation and has the same domain as the relation. The synthesis problem asks for effective uniformization for classes of relations and functions that can be implemented in a specific way.
We consider the synthesis problem for automatic relations over finite words (also called regular or synchronized rational relations) by functions implemented by specific classes of sequential transducers.
It is known that the problem "Given an automatic relation, does it have a uniformization by a subsequential transducer?" is decidable in the two variants where the uniformization can either be implemented by an arbitrary subsequential transducer or it has to be implemented by a synchronous transducer. We introduce a new variant of this problem in which the allowed input/output behavior of the subsequential transducer is specified by a set of synchronizations and prove decidability for a specific class of synchronizations
Formalized proof, computation, and the construction problem in algebraic geometry
An informal discussion of how the construction problem in algebraic geometry
motivates the search for formal proof methods. Also includes a brief discussion
of my own progress up to now, which concerns the formalization of category
theory within a ZFC-like environment
On what I do not understand (and have something to say): Part I
This is a non-standard paper, containing some problems in set theory I have
in various degrees been interested in. Sometimes with a discussion on what I
have to say; sometimes, of what makes them interesting to me, sometimes the
problems are presented with a discussion of how I have tried to solve them, and
sometimes with failed tries, anecdote and opinion. So the discussion is quite
personal, in other words, egocentric and somewhat accidental. As we discuss
many problems, history and side references are erratic, usually kept at a
minimum (``see ... '' means: see the references there and possibly the paper
itself).
The base were lectures in Rutgers Fall'97 and reflect my knowledge then. The
other half, concentrating on model theory, will subsequently appear
Uniformisation Gives the Full Strength of Regular Languages
Given R a binary relation between words (which we treat as a language over a product alphabet AxB), a uniformisation of it is another relation L included in R which chooses a single word over B, for each word over A whenever there exists one. It is known that MSO, the full class of regular languages, is strong enough to define a uniformisation for each of its relations. The quest of this work is to see which other formalisms, weaker than MSO, also have this property. In this paper, we solve this problem for pseudo-varieties of semigroups: we show that no nonempty pseudo-variety weaker than MSO can provide uniformisations for its relations
Topological set theories and hyperuniverses
We give a new set theoretic system of axioms motivated by a topological intuition: The set of subsets of any set is a topology on that set. On the one hand, this system is a common weakening of Zermelo-Fraenkel set theory ZF, the positive set theory GPK and the theory of hyperuniverses. On the other hand, it retains most of the expressiveness of these theories and has the same consistency strength as ZF. We single out the additional axiom of the universal set as the one that increases the consistency strength to that of GPK and explore several other axioms and interrelations between those theories.
Hyperuniverses are a natural class of models for theories with a universal set. The Aleph_0- and Aleph_1-dimensional Cantor cubes are examples of hyperuniverses with additivity Aleph_0, because they are homeomorphic to their hyperspace. We prove that in the realm of spaces with uncountable additivity, none of the generalized Cantor cubes has that property.
Finally, we give two complementary constructions of hyperuniverses which generalize many of the constructions found in the literature and produce initial and terminal hyperuniverses
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