Bartek Klin
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View article: Orbit-Finite-Dimensional Vector Spaces and Weighted Register Automata
Orbit-Finite-Dimensional Vector Spaces and Weighted Register Automata Open
We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automat…
View article: Polyregular Functions on Unordered Trees of Bounded Height
Polyregular Functions on Unordered Trees of Bounded Height Open
We consider injective first-order interpretations that input and output trees of bounded height. The corresponding functions have polynomial output size, since a first-order interpretation can use a -tuple of input nodes to represent a s…
View article: Polyregular functions on unordered trees of bounded height
Polyregular functions on unordered trees of bounded height Open
We consider injective first-order interpretations that input and output trees of bounded height. The corresponding functions have polynomial output size, since a first-order interpretation can use a k-tuple of input nodes to represent a si…
View article: Monadic Monadic Second Order Logic
Monadic Monadic Second Order Logic Open
One of the main reasons for the correspondence of regular languages and monadic second-order logic is that the class of regular languages is closed under images of surjective letter-to-letter homomorphisms. This closure property holds for …
View article: Countdown μ-Calculus
Countdown μ-Calculus Open
We introduce the countdown μ-calculus, an extension of the modal μ-calculus with ordinal approximations of fixpoint operators. In addition to properties definable in the classical calculus, it can express (un)boundedness properties such as…
View article: Orbit-Finite-Dimensional Vector Spaces and Weighted Register Automata
Orbit-Finite-Dimensional Vector Spaces and Weighted Register Automata Open
We develop a theory of vector spaces spanned by orbit-finite sets. Using this theory, we give a decision procedure for equivalence of weighted register automata, which are the common generalization of weighted automata and register automat…
View article: μ-Calculi with Atoms (Invited Talk)
μ-Calculi with Atoms (Invited Talk) Open
Modal μ-calculus is a well-known formalism for describing properties of state-based transition systems. It can define properties such as "[in the current state] p holds, and there is a path where is holds again at some point in the future"…
View article: Definable isomorphism problem
Definable isomorphism problem Open
We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying struc…
View article: Definable isomorphism problem
Definable isomorphism problem Open
We investigate the isomorphism problem in the setting of definable sets (equivalent to sets with atoms): given two definable relational structures, are they related by a definable isomorphism? Under mild assumptions on the underlying struc…
View article: A non-regular language of infinite trees that is recognizable by a sort-wise finite algebra
A non-regular language of infinite trees that is recognizable by a sort-wise finite algebra Open
$\omega$-clones are multi-sorted structures that naturally emerge as algebras for infinite trees, just as $\omega$-semigroups are convenient algebras for infinite words. In the algebraic theory of languages, one hopes that a language is re…
View article: A non-regular language of infinite trees that is recognizable by a sort-wise finite algebra
A non-regular language of infinite trees that is recognizable by a sort-wise finite algebra Open
$\omega$-clones are multi-sorted structures that naturally emerge as algebras for infinite trees, just as $\omega$-semigroups are convenient algebras for infinite words. In the algebraic theory of languages, one hopes that a language is re…
View article: Scalar and Vectorial mu-calculus with Atoms
Scalar and Vectorial mu-calculus with Atoms Open
We study an extension of modal $\mu$-calculus to sets with atoms and we study its basic properties. Model checking is decidable on orbit-finite structures, and a correspondence to parity games holds. On the other hand, satisfiability becom…
View article: Scalar and Vectorial mu-calculus with Atoms
Scalar and Vectorial mu-calculus with Atoms Open
We study an extension of modal $\mu$-calculus to sets with atoms and we study its basic properties. Model checking is decidable on orbit-finite structures, and a correspondence to parity games holds. On the other hand, satisfiability becom…
View article: Codensity Games for Bisimilarity
Codensity Games for Bisimilarity Open
Bisimilarity as an equivalence notion of systems has been central to process theory. Due to the recent rise of interest in quantitative systems (probabilistic, weighted, hybrid, etc.), bisimilarity has been extended in various ways: notabl…
View article: Iterated Covariant Powerset is not a Monad
Iterated Covariant Powerset is not a Monad Open
We prove that the double covariant powerset functor PP does not admit any monad structure. The same applies to the n-fold composition of P for any n>1.
View article: Coalgebraic trace semantics via forgetful logics
Coalgebraic trace semantics via forgetful logics Open
We use modal logic as a framework for coalgebraic trace semantics, and show the flexibility of the approach with concrete examples such as the language semantics of weighted, alternating and tree automata, and the trace semantics of genera…
View article: Expressiveness of Probabilistic Modal Logics, Revisited
Expressiveness of Probabilistic Modal Logics, Revisited Open
Labelled Markov processes are probabilistic versions of labelled transition systems. In general, the state space of a labelled Markov process may be a continuum. Logical characterizations of probabilistic bisimulation and simulation were g…
View article: Modal mu-Calculus with Atoms
Modal mu-Calculus with Atoms Open
We introduce an extension of modal mu-calculus to sets with atoms and study its basic properties. Model checking is decidable on orbit-finite structures, and a correspondence to parity games holds. On the other hand, satisfiability becomes…
View article: SMT Solving for Functional Programming over Infinite Structures
SMT Solving for Functional Programming over Infinite Structures Open
We develop a simple functional programming language aimed at manipulating infinite, but first-order definable structures, such as the countably infinite clique graph or the set of all intervals with rational endpoints. Internally, such set…
View article: Homomorphism Problems for First-Order Definable Structures
Homomorphism Problems for First-Order Definable Structures Open
We investigate several variants of the homomorphism problem: given two relational structures, is there a homomorphism from one to the other? The input structures are possibly infinite, but definable by first-order interpretations in a fixe…