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

## Publications (69)

Article
Full-text available
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...
Chapter
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...
Preprint
Full-text available
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...
Chapter
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...
Preprint
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...
Preprint
Full-text available
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...
Chapter
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...
Chapter
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),...
Preprint
Full-text available
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...
Preprint
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...
Preprint
Full-text available
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),...
Article
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 $\omeg... Article Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited expressiveness, the lack of quantitative features, and the inability to express robustness. There is work on over... Conference Paper Preprint Full-text available Temporal logics for the specification of information-flow properties are able to express relations between multiple executions of a system. The two most important such logics are HyperLTL and HyperCTL*, which generalise LTL and CTL* by trace quantification. It is known that this expressiveness comes at a price, i.e. satisfiability is undecidable fo... Preprint Full-text available We study the expressiveness and succinctness of good-for-games pushdown automata (GFG-PDA) over finite words, that is, pushdown automata whose nondeterminism can be resolved based on the run constructed so far, but independently of the remainder of the input word. We prove that GFG-PDA recognise more languages than deterministic PDA (DPDA) but not... Preprint We present an exponential-time algorithm approximating the minimal lookahead necessary to win an$\omega$-regular delay game. Preprint Full-text available 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... Article Full-text available Preprint 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... Conference Paper Conference Paper Full-text available 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... Article Full-text available 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... Chapter 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... Preprint 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...
Preprint
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...
Article
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...
Preprint
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,...
Preprint
Full-text available
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...
Article
Full-text available
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...
Preprint
Full-text available
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...
Conference Paper
Full-text available
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...
Preprint
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...
Preprint
Full-text available
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...
Preprint
Full-text available
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...
Article
Full-text available
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...
Article
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...
Article
Full-text available
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...
Article
Full-text available
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...
Article
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...
Article
Full-text available
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Article
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...
Conference Paper
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...
Conference Paper
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...
Conference Paper
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...
Article
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...
Conference Paper
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...
Article
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...
Article
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...
Article
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...
Article
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...
Conference Paper
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...
Article
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...
Conference Paper
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...
Conference Paper
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...
Conference Paper
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]. ...
... 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]). ...
... 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]. ...
Citing conference paper
... 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. ...
Citing conference paper
... 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. ...
... 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]. ...