arXiv subjects

Aniello Murano

Publications and source records attributed to Aniello Murano.

At least 37 records · Page 2Linked to original sources

arXiv2022

The Parking Problem: A Game-Theoretic Solution

In this paper, we propose a game-theoretic solution to the parking problem, by exploiting a strategic-reasoning approach for multi-agent systems. Precisely, cars are modeled by agents interacting among them in a multi-player game setting, whose aim is to get a free slot parking-place satisfying their own constraints. The overall assignment is then given as a Nash equilibrium solution. We come up with an algorithm (and its implementation in a tool) that works in quadratic time. We give evidence of the benefits of our approach by running our tool on a large hospital parking space.

cs.MA↗

arXiv2022

Reasoning about Human-Friendly Strategies in Repeated Keyword Auctions

In online advertising, search engines sell ad placements for keywords continuously through auctions. This problem can be seen as an infinitely repeated game since the auction is executed whenever a user performs a query with the keyword. As advertisers may frequently change their bids, the game will have a large set of equilibria with potentially complex strategies. In this paper, we propose the use of natural strategies for reasoning in such setting as they are processable by artificial agents with limited memory and/or computational power as well as understandable by human users. To reach this goal, we introduce a quantitative version of Strategy Logic with natural strategies in the setting of imperfect information. In a first step, we show how to model strategies for repeated keyword auctions and take advantage of the model for proving properties evaluating this game. In a second step, we study the logic in relation to the distinguishing power, expressivity, and model-checking complexity for strategies with and without recall.

cs.GT↗

arXiv2020

Alternating Tree Automata with Qualitative Semantics

We study alternating automata with qualitative semantics over infinite binary trees: alternation means that two opposing players construct a decoration of the input tree called a run, and the qualitative semantics says that a run of the automaton is accepting if almost all branches of the run are accepting. In this paper we prove a positive and a negative result for the emptiness problem of alternating automata with qualitative semantics. The positive result is the decidability of the emptiness problem for the case of Büchi acceptance condition. An interesting aspect of our approach is that we do not extend the classical solution for solving the emptiness problem of alternating automata, which first constructs an equivalent non-deterministic automaton. Instead, we directly construct an emptiness game making use of imperfect information. The negative result is the undecidability of the emptiness problem for the case of co-Büchi acceptance condition. This result has two direct consequences: the undecidability of monadic second-order logic extended with the qualitative path-measure quantifier, and the undecidability of the emptiness problem for alternating tree automata with non-zero semantics, a recently introduced probabilistic model of alternating tree automata.

cs.FL↗

arXiv2020

Optimal Strategies in Weighted Limit Games

We prove the existence and computability of optimal strategies in weighted limit games, zero-sum infinite-duration games with a Büchi-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 that satisfy the specification.

cs.GT↗

arXiv2020

Optimal Strategies in Weighted Limit Games (full version)

cs.GT↗

arXiv2020

Equilibria for Games with Combined Qualitative and Quantitative Objectives

The overall aim of our research is to develop techniques to reason about the equilibrium properties of multi-agent systems. We model multi-agent systems as concurrent games, in which each player is a process that is assumed to act independently and strategically in pursuit of personal preferences. In this article, we study these games in the context of finite-memory strategies, and we assume players' preferences are defined by a qualitative and a quantitative objective, which are related by a lexicographic order: a player first prefers to satisfy its qualitative objective (given as a formula of Linear Temporal Logic) and then prefers to minimise costs (given by a mean-payoff function). Our main result is that deciding the existence of a strict epsilon Nash equilibrium in such games is 2ExpTime-complete (and hence decidable), even if players' deviations are implemented as infinite-memory strategies.

cs.LO↗

arXiv2020

Reasoning about strategies on collapsible pushdown arenas with imperfect information

Strategy Logic with imperfect information (SLiR) is a very expressive logic designed to express complex properties of strategic abilities in distributed systems. Previous work on SLiR focused on finite systems, and showed that the model-checking problem is decidable when information on the control states of the system is hierarchical among the players or components of the system, meaning that the players or components can be totally ordered according to their respective knowledge of the state. We show that moving from finite to infinite systems generated by collapsible (higher-order) pushdown systems preserves decidability, under the natural restriction that the stack content is visible. The proof follows the same lines as in the case of finite systems, but requires to use (collapsible) alternating pushdown tree automata. Such automata are undecidable, but semi-alternating pushdown tree automata were introduced and proved decidable, to study a strategic problem on pushdown systems with two players. In order to tackle multiple players with hierarchical information, we refine further these automata: we define direction-guided (collapsible) pushdown tree automata, and show that they are stable under projection, nondeterminisation and narrowing. For the latter operation, used to deal with imperfect information, stability holds under some assumption that is satisfied when used for systems with visible stack. We then use these automata to prove our main result.

cs.LO↗

arXiv2020

Strategy Logic with Imperfect Information

We introduce an extension of Strategy Logic for the imperfect-information setting, called SLii, and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, this problem is undecidable; but we introduce a syntactical class of "hierarchical instances" for which, intuitively, as one goes down the syntactic tree of the formula, strategy quantifications are concerned with finer observations of the model, and we prove that model-checking SLii restricted to hierarchical instances is decidable. To establish this result we go through QCTL, an intermediary, "low-level" logic much more adapted to automata techniques. QCTL is an extension of CTL with second-order quantification over atomic propositions. We extend it to the imperfect information setting by parameterising second-order quantifiers with observations. While the model-checking problem of QCTLii is, in general, undecidable, we identify a syntactic fragment of hierarchical formulas and prove, using an automata-theoretic approach, that it is decidable. We apply our result to solve complex strategic problems in the imperfect-information setting. We first show that the existence of Nash equilibria for deterministic strategies is decidable in games with hierarchical information. We also introduce distributed rational synthesis, a generalisation of rational synthesis to the imperfect-information setting. Because it can easily be expressed in our logic, our main result provides solution to this problem in the case of hierarchical information.

cs.LO↗

arXiv2020

Dynamic Epistemic Logic Games with Epistemic Temporal Goals

Dynamic Epistemic Logic (DEL) is a logical framework in which one can describe in great detail how actions are perceived by the agents, and how they affect the world. DEL games were recently introduced as a way to define classes of games with imperfect information where the actions available to the players are described very precisely. This framework makes it possible to define easily, for instance, classes of games where players can only use public actions or public announcements. These games have been studied for reachability objectives, where the aim is to reach a situation satisfying some epistemic property expressed in epistemic logic; several (un)decidability results have been established. In this work we show that the decidability results obtained for reachability objectives extend to a much more general class of winning conditions, namely those expressible in the epistemic temporal logic LTLK. To do so we establish that the infinite game structures generated by DEL public actions are regular, and we describe how to obtain finite representations on which we rely to solve them.

cs.LO↗

arXiv2019

Solving Parity Games Using An Automata-Based Algorithm

Parity games are abstract infinite-round games that take an important role in formal verification. In the basic setting, these games are two-player, turn-based, and played under perfect information on directed graphs, whose nodes are labeled with priorities. The winner of a play is determined according to the parities (even or odd) of the minimal priority occurring infinitely often in that play. The problem of finding a winning strategy in parity games is known to be in UPTime $\cap$ CoUPTime and deciding whether a polynomial time solution exists is a long-standing open question. In the last two decades, a variety of algorithms have been proposed. Many of them have been also implemented in a platform named PGSolver. This has enabled an empirical evaluation of these algorithms and a better understanding of their relative merits. In this paper, we further contribute to this subject by implementing, for the first time, an algorithm based on alternating automata. More precisely, we consider an algorithm introduced by Kupferman and Vardi that solves a parity game by solving the emptiness problem of a corresponding alternating parity automaton. Our empirical evaluation demonstrates that this algorithm outperforms other algorithms when the game has a a small number of priorities relative to the size of the game. In many concrete applications, we do indeed end up with parity games where the number of priorities is relatively small. This makes the new algorithm quite useful in practice.

cs.GT↗

arXiv2019

Reasoning about Quality and Fuzziness of Strategic Behaviours

Temporal logics are extensively used for the specification of on-going behaviours of reactive systems. Two significant developments in this area are the extension of traditional temporal logics with modalities that enable the specification of on-going strategic behaviours in multi-agent systems, and the transition of temporal logics to a quantitative setting, where different satisfaction values enable the specifier to formalise concepts such as certainty or quality. We introduce and study FSL---a quantitative extension of SL (Strategy Logic), one of the most natural and expressive logics describing strategic behaviours. The satisfaction value of an FSL formula is a real value in [0,1], reflecting `how much' or `how well' the strategic on-going objectives of the underlying agents are satisfied. We demonstrate the applications of FSL in quantitative reasoning about multi-agent systems, by showing how it can express concepts of stability in multi-agent systems, and how it generalises some fuzzy temporal logics. We also provide a model-checking algorithm for our logic, based on a quantitative extension of Quantified CTL*.

cs.LO↗

arXiv2019

Planning and Synthesis Under Assumptions

In Reasoning about Action and Planning, one synthesizes the agent plan by taking advantage of the assumption on how the environment works (that is, one exploits the environment's effects, its fairness, its trajectory constraints). In this paper we study this form of synthesis in detail. We consider assumptions as constraints on the possible strategies that the environment can have in order to respond to the agent's actions. Such constraints may be given in the form of a planning domain (or action theory), as linear-time formulas over infinite or finite runs, or as a combination of the two. We argue though that not all assumption specifications are meaningful: they need to be consistent, which means that there must exist an environment strategy fulfilling the assumption in spite of the agent actions. For such assumptions, we study how to do synthesis/planning for agent goals, ranging from a classical reachability to goal on traces specified in \LTL and \LTLf/\LDLf, characterizing the problem both mathematically and algorithmically.

cs.LO↗

arXiv2019

Monadic Second-Order Logic with Path-Measure Quantifier is Undecidable

We prove that the theory of Monadic Second-Order logic (MSO) of the infinite binary tree extended with qualitative path-measure quantifier is undecidable. This quantifier says that the set of infinite paths in the tree that satisfies some formula has Lebesgue-measure one. To do this we prove that the emptiness problem of qualitative universal parity tree automata is undecidable. Qualitative means that a run of a tree automaton is accepting if the set of paths in the run that satisfy the acceptance condition has Lebesgue-measure one.

cs.LO↗

arXiv2018

Timed Context-Free Temporal Logics

The paper is focused on temporal logics for the description of the behaviour of real-time pushdown reactive systems. The paper is motivated to bridge tractable logics specialized for expressing separately dense-time real-time properties and context-free properties by ensuring decidability and tractability in the combined setting. To this end we introduce two real-time linear temporal logics for specifying quantitative timing context-free requirements in a pointwise semantics setting: Event-Clock Nested Temporal Logic (EC_NTL) and Nested Metric Temporal Logic (NMTL). The logic EC_NTL is an extension of both the logic CaRet (a context-free extension of standard LTL) and Event-Clock Temporal Logic (a tractable real-time logical framework related to the class of Event-Clock automata). We prove that satisfiability of EC_NTL and visibly model-checking of Visibly Pushdown Timed Automata (VPTA) against EC_NTL are decidable and EXPTIME-complete. The other proposed logic NMTL is a context-free extension of standard Metric Temporal Logic (MTL). It is well known that satisfiability of future MTL is undecidable when interpreted over infinite timed words but decidable over finite timed words. On the other hand, we show that by augmenting future MTL with future context-free temporal operators, the satisfiability problem turns out to be undecidable also for finite timed words. On the positive side, we devise a meaningful and decidable fragment of the logic NMTL which is expressively equivalent to EC_NTL and for which satisfiability and visibly model-checking of VPTA are EXPTIME-complete.

cs.LO↗

arXiv2018

Quantified CTL with imperfect information

Quantified CTL (QCTL) is a well-studied temporal logic that extends CTL with quantification over atomic propositions. It has recently come to the fore as a powerful intermediary framework to study logics for strategic reasoning. We extend it to include imperfect information by parameterising quantifiers with an observation that defines how well they observe the model, thus constraining their behaviour. We consider two different semantics, one related to the notion of no memory, the other to perfect recall. We study the expressiveness of our logic, and show that it coincides with MSO for the first semantics and with MSO with equal level for the second one. We establish that the model-checking problem is Pspace-complete for the first semantics. While it is undecidable for the second one, we identify a syntactic fragment, defined by a notion of hierarchical formula, which we prove to be decidable thanks to an automata-theoretic approach.

cs.LO↗

arXiv2018

Changing Observations in Epistemic Temporal Logic

We study dynamic changes of agents' observational power in logics of knowledge and time. We consider CTL*K, the extension of CTL* with knowledge operators, and enrich it with a new operator that models a change in an agent's way of observing the system. We extend the classic semantics of knowledge for perfect-recall agents to account for changes of observation, and we show that this new operator strictly increases the expressivity of CTL*K. We reduce the model-checking problem for our logic to that for CTL*K, which is known to be decidable. This provides a solution to the model-checking problem for our logic, but its complexity is not optimal. Indeed we provide a direct decision procedure with better complexity.

cs.LO↗

arXiv2018

Decidability results for ATL* with imperfect information and perfect recall

Alternating-time Temporal Logic (ATL*) is a central logic for multiagent systems. Its extension to the imperfect information setting (ATL*i ) is well known to have an undecidable model-checking problem when agents have perfect recall. Studies have thus mostly focused either on agents without memory, or on alternative semantics to retrieve decidability. In this work we establish new decidability results for agents with perfect recall: We first prove a meta-theorem that allows the transfer of decidability results for classes of multiplayer games with imperfect information, such as games with hierarchical observation, to the model-checking problem for ATL*i . We then establish that model checking ATL* with strategy context and imperfect information is decidable when restricted to hierarchical instances.

cs.LO↗

arXiv2018

Reasoning about Knowledge and Strategies under Hierarchical Information

Two distinct semantics have been considered for knowledge in the context of strategic reasoning, depending on whether players know each other's strategy or not. The problem of distributed synthesis for epistemic temporal specifications is known to be undecidable for the latter semantics, already on systems with hierarchical information. However, for the other, uninformed semantics, the problem is decidable on such systems. In this work we generalise this result by introducing an epistemic extension of Strategy Logic with imperfect information. The semantics of knowledge operators is uninformed, and captures agents that can change observation power when they change strategies. We solve the model-checking problem on a class of "hierarchical instances", which provides a solution to a vast class of strategic problems with epistemic temporal specifications on hierarchical systems, such as distributed synthesis or rational synthesis.

cs.LO↗