# Daniel HausmannFriedrich-Alexander-University of Erlangen-Nürnberg | FAU · Chair for Theoretical Computer Science

Daniel Hausmann

Doctor of Engineering

## About

30

Publications

854

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99

Citations

## Publications

Publications (30)

Algorithms for model checking and satisfiability of the modal $\mu$-calculus start by converting formulas to alternating parity tree automata. Thus, model checking is reduced to checking acceptance by tree automata and satisfiability to checking their emptiness. The first reduces directly to the solution of parity games but the second is more compl...

Infinite words over infinite alphabets serve as models of the temporal development of the allocation and (re-)use of resources over linear time. We approach omega-languages over infinite alphabets in the setting of nominal sets, and study languages of infinite bar strings, i.e. infinite sequences of names that feature binding of fresh names; bindin...

It is well-known that the winning region of a parity game with n nodes and k priorities can be computed as a k -nested fixpoint of a suitable function; straightforward computation of this nested fixpoint requires $$\mathcal {O}(n^{\frac{k}{2}})$$ O ( n k 2 ) iterations of the function. Calude et al.’s recent quasipolynomial-time parity game solving...

Logics and automata models for languages over infinite alphabets, such as Freeze LTL and register automata, respectively, serve the verification of processes or documents with data. They relate tightly to formalisms over nominal sets, where names play the role of data. For example, regular nondeterministic nominal automata (RNNA) are equivalent to...

Satisfiability checking for monotone modal logic is known to be (only) NP-complete. We show that this remains true when the logic is extended with alternation-free fixpoint operators as well as the universal modality; the resulting logic – the alternation-free monotone \(\mu \)-calculus with the universal modality – contains both concurrent proposi...

Satisfiability checking for monotone modal logic is known to be (only) NP-complete. We show that this remains true when the logic is extended with aconjunctive and alternation-free fixpoint operators as well as the universal modality; the resulting logic -- the aconjunctive alternation-free monotone $\mu$-calculus with the universal modality -- con...

We discuss expansions of \(\mathsf {CTL}\) with connectives able to express Streett fairness objectives for single paths. We focus on \(\mathsf {(E)SFCTL}\): (Extended) Streett-Fair \(\mathsf {CTL}\) inspired by a seminal paper of Emerson and Lei. Unlike several other fair extensions of \(\mathsf {CTL}\), our entire formalism (not just a subclass o...

We discuss expansions of CTL with connectives able to express Streett fairness objectives for single paths. We focus on (E)SFCTL: (Extended) Streett-Fair CTL inspired by a seminal paper of Emerson and Lei. Unlike several other fair extensions of CTL, our entire formalism (not just a subclass of formulas in some canonical form) allows a succinct emb...

It is well known that the winning region of a parity game with $n$ nodes and $k$ priorities can be computed as a $k$-nested fixpoint of a suitable function; straightforward computation of this nested fixpoint requires $n^{\lceil\frac{k}{2}\rceil+1}$ iterations of the function. The recent parity game solving algorithm by Calude et al. runs in quasip...

The coalgebraic \(\mu \)-calculus provides a generic semantic framework for fixpoint logics with branching types beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the coalgebraic \(\mu \)-calculus includes an exponential time upper bound on satisfiability checking, which however requires a well-beha...

The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics with branching types beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the coalgebraic $\mu$-calculus includes an exponential time upper bound on satisfiability checking, which however requires a well-behaved se...

We introduce a natural notion of limit-deterministic parity automata and present a method that uses such automata to construct satisfiability games for the weakly aconjunctive fragment of the \(\mu \)-calculus. To this end we devise a method that determinizes limit-deterministic parity automata of size n with k priorities through limit-deterministi...

The coalgebraic µ-calculus is an expressive logic that generalizes the modal µ-calculus by interpreting formulas over T-coalgebras rather than Kripke structures. Due to the presence of fixpoint operators, the semantics of µ-calculi is rather involved and satisfiability checking for µ-calculus formulas typically necessitates the use of automata theo...

We introduce a natural notion of limit-deterministic parity automata and present a method that uses such automata to construct satisfiability games for the weakly aconjunctive fragment of the mu-calculus. To this end we devise a method that determinizes limit-deterministic parity automata of size n with k priorities through limit-deterministic B\"u...

Branching-time temporal logics generalizing relational temporal logics such as CTL have been proposed for various system types beyond the purely relational world. This includes, e.g., alternating-time logics, which talk about winning strategies over concurrent game structures, and Parikh's game logic, which is interpreted over monotone neighbourhoo...

The generic modal reasoner CoLoSS covers a wide variety of logics ranging from graded and probabilistic modal logic to coalition logic and conditional logics, being based on a broadly applicable coalgebraic seman- tics and an ensuing general treatment of modal sequent and tableau calculi. Here, we present research into optimisation of the reasoning...

Conditional logics capture default entailment in a modal framework in which non-monotonic implication is a first-class citizen, and in particular can be negated and nested. There is a wide range of axiomatizations of conditionals in the literature, from weak systems such as the basic conditional logic CK, which allows only for equivalent exchange o...

This paper presents work in the context of the certification of a safety component for autonomous service robots, and investigates the potential advantages offered by formally modelling the domain knowledge, specification and implementation in a theorem prover in higher-order logic. This allows safety properties to be stated in an abstract manner c...

This paper presents work in the context of the certification of a safety component for autonomous service robots, and investigates the potential advantages offered by formally modelling the domain knowledge, specification and implementation in a theorem prover in higher-order logic. This allows safety properties to be stated in an abstract manner c...

Recently, various process calculi have been introduced which are suited for the modelling of mobile computation and in particular the mobility of program code; a prominent example is the ambient calculus. Due to the complexity of the involved spatial reduction, there is—in contrast to the situation in standard process algebra—up to now no satisfyin...

Recently, various process calculi have been introduced which are suited for the modelling of mobile computation and in particular the mobility of program code; a prominent example is the ambient calculus. Due to the complexity of the involved spatial reduction, there is — in contrast to the situation in standard process algebra — up to now no sat-...

Coalgebra has in recent years been recognized as the frame- work of choice for the treatment of reactive systems at an appropriate level of generality. Proofs about the reactive behavior of a coalgebraic system typically rely on the method of coinduction. In comparison to 'traditional' coinduction, which has the disadvantage of requiring the invent...

Abstract There is (at this time) no general method,for the representation of (partial) recursive functions in type theories. After a short introduction to algebraic speciflcations, the presentation of (partial) recursive functions in algebraic speciflcations is analyzed in this work. A short overview over type theories is given afterwards and an ap...