# Martin Zimmermann's research while affiliated with Aalborg University and other places

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## Publications (69)

Runtime monitoring is commonly used to detect the violation of desired properties in safety critical cyber-physical systems by observing its executions. Bauer et al. introduced an influential framework for monitoring Linear Temporal Logic (LTL) properties based on a three-valued semantics for a finite execution: the formula is already satisfied by...

While most of the current synthesis algorithms only focus on correctness-by-construction, ensuring robustness has remained a challenge. Hence, in this paper, we address the robust-by-construction synthesis problem by considering the specifications to be expressed by a robust version of Linear Temporal Logic (LTL), called robust LTL (rLTL). rLTL has...

Parikh automata extend finite automata by counters that can be tested for membership in a semilinear set, but only at the end of a run. Thereby, they preserve many of the desirable properties of finite automata. Deterministic Parikh automata are strictly weaker than nondeterministic ones, but enjoy better closure and algorithmic properties. This st...

In this paper we revisit monitoring real-time systems with respect to properties expressed either in Metric Interval Temporal Logic or as Timed Büchi Automata. We offer efficient symbolic online monitoring algorithms in a number of settings, exploiting so-called zones well-known from efficient model checking of Timed Automata. The settings consider...

Parikh automata extend finite automata by counters that can be tested for membership in a semilinear set, but only at the end of a run, thereby preserving many of the desirable algorithmic properties of finite automata. Here, we study the extension of the classical framework onto infinite inputs: We introduce reachability, safety, B\"uchi, and co-B...

In this paper we revisit monitoring real-time systems with respect to properties expressed either in the Metric Interval Temporal Logic or as Timed B\"uchi Automata. We offer efficient symbolic online monitoring algorithms in a number of settings, exploiting so-called zones well-known from efficient model checking of Timed Automata. The settings co...

Nfer is a rule-based language for abstracting event streams into a hierarchy of intervals with data. Nfer has multiple implementations and has been applied in the analysis of spacecraft telemetry and autonomous vehicle logs. This work provides the first complexity analysis of nfer evaluation, i.e., the problem of deciding whether a given interval i...

It is widely accepted that every system should be robust in that “small” violations of environment assumptions should lead to “small” violations of system guarantees, but it is less clear how to make this intuition mathematically precise. While significant efforts have been devoted to providing notions of robustness for Linear Temporal Logic (LTL),...

While most of the current synthesis algorithms only focus on correctness-by-construction, ensuring robustness has remained a challenge. Hence, in this paper, we address the robust-by-construction synthesis problem by considering the specifications to be expressed by a robust version of Linear Temporal Logic (LTL), called robust LTL (rLTL). rLTL has...

Nfer is a rule-based language for abstracting event streams into a hierarchy of intervals with data. Nfer has multiple implementations and has been applied in the analysis of spacecraft telemetry and autonomous vehicle logs. This work provides the first complexity analysis of nfer evaluation, i.e., the problem of deciding whether a given interval i...

It is widely accepted that every system should be robust in that "small" violations of environment assumptions should lead to "small" violations of system guarantees, but it is less clear how to make this intuition mathematically precise. While significant efforts have been devoted to providing notions of robustness for Linear Temporal Logic (LTL),...

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 $\omeg...

Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited expressiveness, the lack of quantitative features, and the inability to express robustness. There is work on over...

Temporal logics for the specification of information-flow properties are able to express relations between multiple executions of a system. The two most important such logics are HyperLTL and HyperCTL*, which generalise LTL and CTL* by trace quantification. It is known that this expressiveness comes at a price, i.e. satisfiability is undecidable fo...

We study the expressiveness and succinctness of good-for-games pushdown automata (GFG-PDA) over finite words, that is, pushdown automata whose nondeterminism can be resolved based on the run constructed so far, but independently of the remainder of the input word. We prove that GFG-PDA recognise more languages than deterministic PDA (DPDA) but not...

We present an exponential-time algorithm approximating the minimal lookahead necessary to win an $\omega$-regular delay game.

We prove the existence and computability of optimal strategies in weighted limit games, zero-sum infinite-duration games with a B\"uchi-style winning condition requiring to produce infinitely many play prefixes that satisfy a given regular specification. Quality of plays is measured in the maximal weight of infixes between successive play prefixes...

We prove the existence and computability of optimal strategies in weighted limit games, zero-sum infinite-duration games with a B\"uchi-style winning condition requiring to produce infinitely many play prefixes that satisfy a given regular specification. Quality of plays is measured in the maximal weight of infixes between successive play prefixes...

Runtime monitoring is commonly used to detect the violation of desired properties in safety critical cyber-physical systems by observing its executions. Bauer et al. introduced an influential framework for monitoring Linear Temporal Logic (LTL) properties based on a three-valued semantics: the formula is already satisfied by the given prefix, it is...

Recently, Dallal, Neider, and Tabuada studied a generalization of the classical game-theoretic model used in program synthesis, which additionally accounts for unmodeled intermittent disturbances. In this extended framework, one is interested in computing optimally resilient strategies, i.e., strategies that are resilient against as many disturbanc...

We investigate the satisfaction of specifications in Prompt Linear Temporal Logic (\({\text {Prompt-LTL}}\)) by concurrent systems. Prompt-LTL is an extension of LTL that allows to specify parametric bounds on the satisfaction of eventualities, thus adding a quantitative aspect to the specification language. We establish a connection between bounde...

We introduce good-for-games $\omega$-pushdown automata ($\omega$-GFG-PDA). These are automata whose nondeterminism can be resolved based on the run constructed thus far. Good-for-gameness enables automata to be composed with games, trees, and other automata, applications which otherwise require deterministic automata. Our main results show that $\o...

Infinite-duration games with disturbances extend the classical framework of infinite-duration games, which captures the reactive synthesis problem, with a discrete measure of resilience against non-antagonistic disturbances, i.e., unmodeled situations in which the actual controller action differs from the intended one. For games played on finite ar...

What is a finite-state strategy in a delay game? We answer this surprisingly non-trivial question by presenting a very general framework that allows to remove delay: finite-state strategies exist for all winning conditions where the resulting delay-free game admits a finite-state strategy. The framework is applicable to games whose winning conditio...

We investigate the satisfaction of specifications in Prompt Linear Temporal Logic (Prompt-LTL) by concurrent systems. Prompt-LTL is an extension of LTL that allows to specify parametric bounds on the satisfaction of eventualities, thereby adding a quantitative aspect to the specification language. We establish a connection between bounded fairness,...

Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited expressiveness, the lack of quantitative features, and the inability to express robustness. There is work on over...

Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited expressiveness, the lack of quantitative features, and the inability to express robustness. There is work on over...

HyperLTL, the extension of Linear Temporal Logic by trace quantifiers, is a uniform framework for expressing information flow policies by relating multiple traces of a security-critical system. HyperLTL has been successfully applied to express fundamental security policies like noninterference and observational determinism, but has also found appli...

Linear Temporal Logic (LTL) is the standard specification language for reactive systems and successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited expressiveness, the lack of quantitative features, and the inability to express robustness. Typically, each one of t...

Runtime verification is commonly used to detect and, if possible, react to the violation of desired properties in safety critical systems. Also common is the use of temporal logics to specify the desired properties. However, if properties are expressed in two-valued logics, such as Linear-time Temporal Logic (LTL), monitoring them often yields insu...

We give a direct polynomial-time reduction from parity games played over the configuration graphs of collapsible pushdown systems to safety games played over the same class of graphs. That a polynomial-time reduction would exist was known by complexity theory. Coming up with a direct reduction, however, has been an open problem. Our solution to the...

We determine the complexity of counting models of bounded size of specifications expressed in linear-time temporal logic. Counting word-models is #P-complete, if the bound is given in unary, and as hard as counting accepting runs of nondeterministic polynomial space Turing machines, if the bound is given in binary. Counting tree-models is as hard a...

Quantitative extensions of parity games have recently attracted significant
interest. These extensions include parity games with energy and payoff
conditions as well as finitary parity games and their generalization to parity
games with costs. Finitary parity games enjoy a special status among these
extensions, as they offer a native combination of...

We continue the investigation of parameterized extensions of linear temporal logic (LTL) that retain the attractive algorithmic properties of LTL: a polynomial space model checking algorithm and a doubly-exponential time algorithm for solving games. Alur et al. and Kupferman et al. showed that this is the case for parametric LTL (PLTL) and PROMPT-L...

We develop team semantics for Linear Temporal Logic (LTL) to express hyperproperties, which have recently been identified as a key concept in the verification of information flow properties. Conceptually, we consider an asynchronous and a synchronous variant of team semantics. We study basic properties of this new logic and classify the computation...

We consider the synthesis of distributed implementations for specifications in parameterized temporal logics such as PROMPT-LTL, which extends LTL by temporal operators equipped with parameters that bound their scope. For single process synthesis it is well-established that such parametric extensions do not increase worst-case complexities. For syn...

What is a finite-state strategy in a delay game? We answer this surprisingly non-trivial question and present a very general framework for computing such strategies: they exist for all winning conditions that are recognized by automata with acceptance conditions that satisfy a certain aggregation property. Our framework also yields upper bounds on...

We demonstrate the usefulness of adding delay to infinite games with quantitative winning conditions. In a delay game, one of the players may delay her moves to obtain a lookahead on her opponent's moves. We show that determining the winner of delay games with winning conditions given by parity automata with costs is EXPTIME-complete and that expon...

We consider the synthesis of distributed implementations for specifications in Prompt Linear Temporal Logic (PROMPT-LTL), which extends LTL by temporal operators equipped with parameters that bound their scope. For single process synthesis it is well-established that such parametric extensions do not increase worst-case complexities.
For synchrono...

We introduce Parametric Linear Dynamic Logic (PLDL), which extends Linear Dynamic Logic (LDL) by adding temporal operators equipped with parameters that bound their scope. LDL itself was proposed as an extension of Linear Temporal Logic (LTL) that is able to express all ω-regular specifications while still maintaining many of LTL's desirable proper...

The winning condition of a parity game with costs requires an arbitrary, but fixed bound on the distance between occurrences of odd colors and the next occurrence of a larger even one. Such games quantitatively extend parity games while retaining most of their attractive properties, i.e, determining the winner is in NP and co-NP and one player has...

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent's moves. We consider delay games with winning conditions expressed in weak monadic second order logic with the unbounding quantifier, which is able to express (un)boundedness properties. We show that it is decidable wh...

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent's moves. Recently, such games with quantitative winning conditions in weak MSO with the unbounding quantifier were studied, but their properties turned out to be unsatisfactory. In particular, unbounded lookahead might...

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent’s moves. For ω-regular winning conditions it is known that such games can be solved in doubly-exponential time and that doubly-exponential lookahead is sufficient. We improve upon both results by giving an exponential...

We introduce Visibly Linear Dynamic Logic (VLDL), which is an extension of
Linear Dynamic Logic (LDL) with temporal operators that are guarded by
nondeterministic visibly pushdown automata. We prove that VLDL describes
exactly the visibly pushdown languages over infinite words, which makes it
strictly more powerful than LTL and LDL and able to expr...

In this short note, we consider the optimization variant of the realizability
problem for specifications in Prompt Linear Temporal Logic (Prompt-LTL), which
extends Linear Temporal Logic (LTL) by the prompt eventually operator whose
scope is bounded by a parametric bound. In the realizability optimization
problem, one is interested in computing the...

Energy games are infinite two-player games played in weighted arenas with quantitative objectives that restrict the consumption of a resource modeled by the weights, e.g., a battery that is charged and drained. Typically, upper and/or lower bounds on the battery capacity are part of the problem description. Here, we consider the problem of determin...

Delay games are two-player games of infinite duration in which one player may
delay her moves to obtain a lookahead on her opponent's moves. We consider
delay games with winning conditions expressed in weak monadic second order
logic with the unbounding quantifier (WMSO+U), which is able to express
(un)boundedness properties. It is decidable whethe...

We consider the synthesis of distributed implementations for specifications
in Parametric Linear Temporal Logic (PLTL). PLTL extends LTL by temporal
operators equipped with parameters that bound their scope. For single process
synthesis it is well-established that such parametric extensions do not
increase worst-case complexities. For synchronous s...

We introduce Parametric Linear Dynamic Logic (PLDL), which extends Linear
Dynamic Logic (LDL) by temporal operators equipped with parameters that bound
their scope. LDL itself was proposed as an extension of Linear Temporal Logic
(LTL) that is able to express all omega-regular specifications while still
maintaining many of LTL's desirable propertie...

We investigate determinacy of delay games with Borel winning conditions,
infinite-duration two-player games in which one player may delay her moves to
obtain a lookahead on her opponent's moves.
First, we prove determinacy of such games with respect to a fixed evolution
of the lookahead. However, strategies in such games may depend on information
a...

Delay games are two-player games of infinite duration in which one player may
delay her moves to obtain a lookahead on her opponent's moves. We consider
delay games with winning conditions expressed in weak monadic second order
logic with the unbounding quantifier, which is able to express (un)boundedness
properties.
We show that it is decidable wh...

Delay games are two-player games of infinite duration in which one player may
delay her moves to obtain a lookahead on her opponent's moves. For
omega-regular winning conditions, it is known that such games can be solved in
doubly-exponential time and that doubly-exponential lookahead is sufficient.
We improve upon both results by giving an exponen...

We determine the complexity of counting models of bounded size of
specifications expressed in Linear-time Temporal Logic. Counting word models is
#P-complete, if the bound is given in unary, and as hard as counting accepting
runs of nondeterministic polynomial space Turing machines, if the bound is
given in binary. Counting tree models is as hard a...

We introduce Parametric Linear Dynamic Logic (PLDL), which extends Linear
Dynamic Logic (LDL) by temporal operators equipped with parameters that bound
their scope. LDL was proposed as an extension of Linear Temporal Logic (LTL)
that is able to express all $\omega$-regular specifications while still
maintaining many of LTL's desirable properties li...

We show the solvability of an optimization problem on infinite two-player games. The winning conditions are of the “request-response” format, i.e. conjunctions of conditions of the form “if a state with property Q is visited, then later a state with property P is visited”. We ask for solutions that do not only guarantee the satisfaction of such con...

We continue the investigation of finite-duration variants of
infinite-duration games by extending known results for games played on finite
graphs to those played on infinite ones. In particular, we establish an
equivalence between pushdown parity games and a finite-duration variant. This
allows us to determine the winner of a pushdown parity game b...

We transform a Muller game with n vertices into a safety game with (n!)^3
vertices whose solution allows to determine the winning regions of the Muller
game and to compute a finite-state winning strategy for one player. This yields
a novel antichain-based memory structure and a natural notion of permissive
strategies for Muller games. Moreover, we...

We study two-player games played on finite graphs equipped with costs on
edges and introduce two winning conditions, cost-parity and cost-Streett, which
require bounds on the cost between requests and their responses. Both
conditions generalize the corresponding classical omega-regular conditions and
the corresponding finitary conditions. For parit...

We consider two-player games played on finite graphs equipped with costs on edges and introduce two winning conditions, cost-parity and cost-Streett, which require bounds on the cost between requests and their responses. Both conditions generalize the corresponding classical ω-regular conditions as well as the corresponding finitary conditions. For...

Parameterized linear temporal logics are extensions of Linear Temporal Logic (LTL) by temporal operators equipped with variables that bound their scope. In model-checking, such specifications were introduced as “PLTL” by Alur et al. and as “PROMPT-LTL” by Kupferman et al. We show how to determine in doubly-exponential time, whether a player wins a...

We consider graph games of infinite duration with winning conditions in parameterized linear temporal logic, where the temporal operators are equipped with variables for time bounds. In model checking such specifications were introduced as "PLTL" by Alur et al. and (in a different version called "PROMPT-LTL") by Kupferman et al.. We present an algo...

We continue the investigation of delay games, infinite games in which one player may postpone her moves for some time to obtain a lookahead on her opponent’s moves. We show that the problem of determining the winner of such a game is undecidable for deterministic context-free winning conditions. Furthermore, we show that the necessary lookahead to...

This work considers a finite-duration variant of Muller games, and their connection to infinite-duration Muller games. In particular, it studies the question of how long a finite-duration Muller game must be played before the winner of the finite-duration game is guaranteed to be able to win the corresponding infinite-duration game. Previous work b...

We introduce a novel winning condition for infinite two- player games on graphs which extends the request-response condition and better matches concrete applications in scheduling or project plan- ning. In a poset game, a request has to be responded by multiple events in an ordering over time that is compatible with a given partial ordering of the...

## Citations

... The notion of history-determinism emerged independently in the setting of cost automata, that can capture all regular cost functions as opposed to their deterministic version [10]. Recently, history-determinism has been studied in other quantitative settings [7,8], as well as infinite-state systems such as pushdown automata [13,26], Parikh automata [12], and timed automata [14]. ...

Reference: On History-Deterministic One-Counter Nets

... One of rLTL's key features is its syntactic similarity to LTL, which allows for a seamless and transparent transition from specifications expressed in LTL to specifications expressed in rLTL. Moreover, it is worth mentioning that rLTL has spawned numerous follow-up works, including rLTL model checking [2,3,4], rLTL runtime monitoring [21], and robust extensions of prompt LTL and Linear Dynamic Logic [27], as well as CTL [22]. ...

... This property makes history-deterministic automata suitable for the composition with games, trees, and other automata, applications which classically require deterministic automata. History-determinism has been studied in the context of regular [1,21,26], pushdown [19,27], quantitative [3,9], and timed automata [20]. For automata that can be determinized, history-determinism offers the potential for succinctness (e.g., co-Büchi automata [26]) while for automata that cannot be determinized, it even offers the potential for increased expressiveness (e.g., pushdown automata [19,27]). ...

Reference: History-deterministic Parikh Automata

... One of rLTL's key features is its syntactic similarity to LTL, which allows for a seamless and transparent transition from specifications expressed in LTL to specifications expressed in rLTL. Moreover, it is worth mentioning that rLTL has spawned numerous follow-up works, including rLTL model checking [2,3,4], rLTL runtime monitoring [21], and robust extensions of prompt LTL and Linear Dynamic Logic [27], as well as CTL [22]. ...

... Finally, let us highlight that preliminary results on adaptive strategies have been presented as a poster at the 24th ACM International Conference on Hybrid Systems: Computation and Control [23]. ...

... These assumptions are relaxed in [20], whereby players still have access to a broadcast channel, but transmissions are performed asynchronously. In addition, ref. [20] showed that the schemes of [9,12] are not exactly Nash equilibria if players are allowed to perform a superpolynomial number of computations-which is not at all a given requirement in games according to game-theory literature (i.e., some games are even assumed to be infinite [21]). Ref. [20] thus presented a scheme that is a Nash equilibrium in an information-theoretic sense by drawing shares from an unbounded domain. ...

... This is obtained through five different verdicts (instead of the standard three), which quantitatively denote how much the property has been violated. It is important to note that in rLTL, all properties become monitorable [23]; simply because the resulting monitor does not look for the complete satisfaction (resp., violation) of the property, but it settles for a certain degree of satisfaction (resp., violation) of the latter. ...

Reference: Ain't No Stopping Us Monitoring Now

... An asynchronous implementation can be modelled in automata-theoretic terms as a transducer which, whenever it reads an input i ∈ Σ, produces none or several outputs, i.e. a finite word u ∈ Γ * . Generalizations of reactive system synthesis to asynchronous implementations have been considered in [HKT12,FLZ11,WZ20]. In these works however, the specification is still synchronous, given by an automaton which strictly alternates between reading input and output symbols. ...

... In contrast, no such choices are required in rLTL. Finally, it is worth mentioning that extensions similar to rLTL have been proposed for other temporal logics, such as prompt LTL and linear dynamic logic [50,51]. ...

... In contrast, no such choices are required in rLTL. Finally, it is worth mentioning that extensions similar to rLTL have been proposed for other temporal logics, such as prompt LTL and linear dynamic logic [50,51]. ...