# Giuseppe Perelli's research while affiliated with Sapienza University of Rome and other places

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## Publications (54)

Rational verification refers to the problem of checking which temporal logic properties hold of a concurrent/multiagent system, under the assumption that agents in the system choose strategies that form a game theoretic equilibrium. Rational verification can be understood as a counterpart to model checking for multiagent systems, but while classica...

Rational verification refers to the problem of checking which temporal logic properties hold of a concurrent multiagent system, under the assumption that agents in the system choose strategies that form a game-theoretic equilibrium. Rational verification can be understood as a counterpart to model checking for multiagent systems, but while classica...

Norms have been widely proposed to coordinate and regulate multi-agent systems (MAS) behaviour. We consider the problem of synthesising and revising the set of norms in a normative MAS to satisfy a design objective expressed in Alternating Time Temporal Logic (ATL*). ATL* is a well-established language for strategic reasoning, which allows the spec...

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 contex...

We provide a survey of the state of the art of rational verification: the problem of checking whether a given temporal logic formula ϕ is satisfied in some or all game-theoretic equilibria of a multi-agent system – that is, whether the system will exhibit the behavior ϕ represents under the assumption that agents within the system act rationally in...

Trace Alignment is a prominent problem in Declarative Process Mining, which consists in identifying a minimal set of modifications that a log trace (produced by a system under execution) requires in order to be made compliant with a temporal specification. In its simplest form, log traces are sequences of events from a finite alphabet and specifica...

Temporal logics over finite traces, such as LTLf and its extension LDLf, have been adopted in several areas, including Business Process Management (BPM), to check properties of processes whose executions have an unbounded, but finite, length. These logics express properties of single traces in isolation, however, especially in BPM it is also of int...

In game theory, mechanism design is concerned with the design of incentives so that a desired outcome of the game can be achieved. In this paper, we study the design of incentives so that a desirable equilibrium is obtained, for instance, an equilibrium satisfying a given temporal logic property -- a problem that we call equilibrium design. We base...

We study the impact of the need for the agent to obligatorily instruct the action stop in her strategies. More specifically we consider synthesis (i.e., planning) for LTLf goals under LTL assumptions in the case the agent must mandatorily stop at a certain point. We show that this obligation makes it impossible to exploit the liveness part of the L...

We define and investigate a novel notion of expressiveness for temporal logics that is based on game theoretic equilibria of multi-agent systems. We use iterated Boolean games as our abstract model of multi-agent systems [Gutierrez et al. 2013, 2015a]. In such a game, each agent has a goal , represented using (a fragment of) Linear Temporal Logic (...

In this paper we introduce Behavioral QLTL, which is a ``behavioral'' variant of linear-time temporal logic on infinite traces with second-order quantifiers. Behavioral QLTL is characterized by the fact that the functions that assign the truth value of the quantified propositions along the trace can only depend on the past. In other words such func...

Cost-parity games are a fundamental tool in system design for the analysis of reactive and distributed systems that recently have received a lot of attention from the formal methods research community. They allow to reason about the time delay on the requests granted by systems, with a bounded consumption of resources, in their executions.
In this...

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 contex...

In the context of multi-agent systems, the rational verification problem is concerned with checking which temporal logic properties will hold in a system when its constituent agents are assumed to behave rationally and strategically in pursuit of individual objectives. Typically, those objectives are expressed as temporal logic formulae which the r...

Linear Dynamic Logic on finite traces LDLf is a powerful logic for reasoning about the behaviour of concurrent and multi-agent systems. In this paper, we investigate techniques for both the characterisation and verification of equilibria in multi-player games with goals/objectives expressed using logics based on LDLf. This study builds upon a gener...

We propose a formalism to model and reason about multi-agent systems. We allow agents to interact and communicate in different modes so that they can pursue joint tasks; agents may dynamically synchronize, exchange data, adapt their behaviour, and reconfig-ure their communication interfaces. The formalism defines a local behaviour based on shared v...

In the context of multi-agent systems, the rational verification problem is concerned with checking which temporal logic properties will hold in a system when its constituent agents are assumed to behave rationally and strategically in pursuit of individual objectives. Typically, those objectives are expressed as temporal logic formulae which the r...

Linear Dynamic Logic on finite traces (LDLF) is a powerful logic for reasoning about the behaviour of concurrent and multi-agent systems. In this paper, we investigate techniques for both the characterisation and verification of equilibria in multi-player games with goals/objectives expressed using logics based on LDLF. This study builds upon a gen...

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 p...

We introduce and study SL[F], a quantitative extension of SL (Strategy Logic), one of the most natural and expressive logics describing strategic behaviours. The satisfaction value of an SL[F] 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 demons...

Rational verification involves checking which temporal logic properties hold of a concurrent and multiagent system, under the assumption that agents in the system choose strategies in game theoretic equilibrium. Rational verification can be understood as a counterpart of model checking for multiagent systems, but while model checking can be done in...

Modern computer systems are inherently distributed and feature autonomous and collaborative behaviour of multicomponent with global goals. These goals are expressed in terms of the combined behaviour of different components that are usually deployed in dynamic and evolving environments. It is therefore crucial to provide techniques to generate prog...

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 quantitati...

We present EVE (Equilibrium Verification Environment), a formal verification tool for the automated analysis of temporal equilibrium properties of concurrent and multi-agent systems. In EVE, systems are modelled using the Simple Reactive Module Language (SRML) as a collection of independent system components (players/agents in a game) and players’...

We introduce Cycle-CTL⋆, an extension of CTL⋆ with cycle quantifications that are able to predicate over cycles. The introduced logic turns out to be very expressive. Indeed, we prove that it strictly extends CTL⋆ and is orthogonal to μCALCULUS. We also give an evidence of its usefulness by providing few examples involving non-regular properties. W...

Game theory provides a well-established framework for the analysis of concurrent and multi-agent systems. The basic idea is that concurrent processes (agents) can be understood as corresponding to players in a game; plays represent the possible computation runs of the system; and strategies define the behaviour of agents. Typically, strategies are...

In Rational Synthesis, we consider a multi-agent system in which some of the agents are controllable and some are not. All agents have objectives, and the goal is to synthesize strategies for the controllable agents so that their objectives are satisfied, assuming rationality of the uncontrollable agents. Previous work on rational synthesis conside...

Reactive Modules is a high-level modelling language for concurrent, distributed, and multi-agent systems, which is used in a number of practical model checking tools. Reactive Modules Games are a game-theoretic extension of Reactive Modules, in which system components are assumed to act strategically in an attempt to satisfy a temporal logic formul...

Cost-parity games are a fundamental tool in system design for the analysis of reactive and distributed systems that recently have received a lot of attention from the formal methods research community.
They allow to reason about the time delay on the requests granted by systems, with a bounded consumption of resources, in their executions.
In this...

We study concurrent games with finite-memory strategies where players are given a Buchi and a mean-payoff objective, which are related by a lexicographic order: a player first prefers to satisfy its Buchi objective, and then prefers to minimise costs, which are given by a mean-payoff function. In particular, we show that deciding the existence of a...

Strategy Logic (SL, for short) has been introduced by Mogavero, Murano, and
Vardi as a useful formalism for reasoning explicitly about strategies, as
first-order objects, in multi-agent concurrent games. This logic turns out to
be very powerful, subsuming all major previously studied modal logics for
strategic reasoning, including ATL, ATL*, and th...

Model checking is a powerful method widely explored in formal verification. Given a model of a system, e.g., a Kripke structure, and a formula specifying its expected behaviour, one can verify whether the system meets the behaviour by checking the formula against the model. Classically, system behaviour is expressed by a formula of a temporal logic...

Temporal logic is a very powerful formalism deeply investigated and used in formal system design and verification. Its application usually reduces to solving specific decision problems such as model checking and satisfiability. In these kind of problems, the solution often requires detecting some specific properties over cycles. For instance, this...

Synthesis is the automated construction of a system from its specification. The system has to satisfy its specification in all possible environments. The environment often consists of agents that have objectives of their own. Thus, it makes sense to soften the universal quantification on the behavior of the environment and take the objectives of it...

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 p...

In this work we build on these models to look at social influence from a strategic perspective. We do so by introducing a new class of games, called games of influence. Specifically, a game of influence is an infinite repeated game with incomplete information in which, at each stage of interaction, an agent can make her opinions visible (public) or...

In this work we build on these models to look at social influence from a strategic perspective. We do so by introducing a new class of games, called games of influence. Specifically, a game of influence is an infinite repeated game with incomplete information in which, at each stage of interaction, an agent can make her opinions visible (public) or...

We introduce a novel notion of expressiveness for temporal logics that is based on game theoretic properties of multi-agent systems. We focus on iterated Boolean games, where each agent i has a goal γi, represented using (a fragment of) Linear Temporal Logic (LTL). The goal γi captures agent i's preferences: the models of γi represent system behavi...

Reactive Modules is a high-level modelling language for concurrent , distributed, and multi-agent systems, which is used in a number of practical model checking tools. Reactive Modules Games are a game-theoretic extension of Reactive Modules, in which agents in a system are assumed to act strategically in an attempt to satisfy a temporal logic form...

Rational verification is concerned with establishing whether a given temporal logic formula φ is satisfied in some or all equilibrium computations of a multi-agent system – that is, whether the system will exhibit the behaviour φ under the assumption that agents within the system act rationally in pursuit of their preferences. After motivating and...

We consider the problem of planning paths of multiple agents in a dynamic but predictable environment. Typical scenarios are evacuation, reconfiguration, and containment. We present a novel representation of abstract path-planning problems in which the stationary environment is explicitly coded as a graph while the dynamic environment is treated as...

In this paper we investigate the model-checking problem of pushdown multi-agent systems for ATL specifications. To this aim, we introduce pushdown game structures over which ATL formulas are interpreted.

Synthesis is the automated construction of a system from its specification. The system has to satisfy its specification in all possible environments. The environment often consists of agents that have objectives of their own. Thus, it makes sense to soften the universal quantification on the behavior of the environment and take the objectives of it...

Model checking is a powerful method widely explored in formal verification. Given a model of a system, e.g. A Kripke structure, and a formula specifying its expected behavior, one can verify whether the system meets the behavior by checking the formula against the model. Classically, system behavior is given as a formula of a temporal logic, such a...

In open systems verification, to formally check for reliability, one needs an appropriate formalism to model the interaction between agents and express the correctness of the system no matter how the environment behaves. An important contribution in this context is given by modal logics for strategic ability, in the setting of multiagent games, suc...

Hilbert's Entscheidungsproblem has given rise to a broad and productive line
of research in mathematical logic, where the classification process of
decidable classes of first-order sentences represent only one of the remarkable
results. According to the criteria used to identify the particular classes of
interest, this process was declined into sev...

Strategy Logic (Sl, for short) has been recently introduced by Mogavero, Murano, and Vardi as a formalism for reasoning explicitly about strategies, as first-order objects, in multi-agent concurrent games. This logic turns out to be very powerful, strictly subsuming all major previously studied modal logics for strategic reasoning, including Atl, A...

Strategy Logic (SL, for short) has been recently introduced by Mogavero,
Murano, and Vardi as a useful formalism for reasoning explicitly about
strategies, as first-order objects, in multi-agent concurrent games. This logic
turns to be very powerful, subsuming all major previously studied modal logics
for strategic reasoning, including ATL, ATL*, a...

In open systems verification, to formally check for reliability, one needs an
appropriate formalism to model the interaction between agents and express the
correctness of the system no matter how the environment behaves. An important
contribution in this context is given by modal logics for strategic ability, in
the setting of multi-agent games, su...

## Citations

... In the context of multiagent systems, rational verification forms a natural counterpart of model checking [16,17,33]. This is the problem of checking whether a given property φ, expressed as a temporal logic formula, is satisfied in a computation of a system that might be generated if agents within the system choose strategies for selecting actions that form a game-theoretic equilibrium. ...

Reference: On the complexity of rational verification

... linear temporal logic (LTL) [76], also the more expressive linear dynamic logic [61], alternating time logic [3], and mucalculus [24,65] have been investigated on semantics based on finite traces [28,29,51,55,68]. To deal with uncertainty in dynamic systems, a probabilistic version of LTL over finite traces has been proposed as well [70], while a recent paper addresses problems in declarative process mining by introducing metric temporal logic on finite traces [50]. Significant areas of applications for LTL on finite traces are indeed in the planning domain [23, 34, 37-39, 42, 49], in (declarative) business process modelling, as well as in runtime verification and monitoring [25,27,41,52,77]. ...

... Hence, representing the relative order of the events is quite natural in a sequence data model. This level of abstraction, of viewing traces as sequences of abstract events, is often assumed when working with temporal and dynamic logics [16,30,17]. Sequence Datalog [3,6,27] is an extension of the query language Datalog, to work with sequences as first class citizens. ...

... This infinite sequence of valuations is then used to determine which temporal goals are satisfied and which are not. Finding Nash equilibria in such games corresponds to a useful method of analysis of the systems that these games model; as such, there is a very large of body finding Nash equilibria when agents' goals are given by an infinite-horizon logic such as Linear Time Temporal Logic (LTL) (Wooldridge 2009;Gutierrez et al. 2020;Mogavero et al. 2014;Grädel, Thomas, and Wilke 2002;Abate et al. 2021). ...

... Our results are important because they show that for several significant settings, rational verification can be done with polynomial space algorithms. These results are much more attractive than in the general case, and hold out the hope of efficient practical tools (c.f. the Equilibrium Verification Environment (EVE) [20,21], a tool for the automated analysis of temporal equilibrium properties). Further practical implementations thus seem to be a natural step forward towards the deployment of rational verification in more realistic scenarios. ...

Reference: On the complexity of rational verification

... In this paper, we are interested in concurrenct systems where events are affected by changes happening to non-participants. This situation, which we call in general reconfiguration, arises in two types of very different models of concucrrent systems: Channeled Transition Systems (CTS) [5,4] 1 and Petri net with inhibitor arcs (PTI-nets) [16,12,9]. In the first, processes connect and disconnect to channels during execution and by doing so disable and enable communications on these channels in which they ultimately do not participate. ...

Reference: A PO Characterisation of Reconfiguration

... To do this, we need to introduce the notion of the punishment value in a multi-player mean-payoff game; cf., [30,31]. The punishment value, pun i (s), of a player i in a given state s can be thought of as the worst value the other players can impose on a player at a given state. ...

... While agents still create an infinite trace by setting their variables at every time step, satisfaction is considered over finite prefixes. The analogous problem of finding Nash equilibria in iterated boolean games in which each agent has been given a finite-horizon temporal goal has recently begun to receive attention (Rajasekaran and Vardi 2021;Gutierrez, Perelli, and Wooldridge 2017). ...

... where | | is the number of symbols in , except by parentheses. If is a -ary function in F , then | | = + 1. [18] proposes a quantitative semantics for Strategy Logic, in which strategies are functions mapping histories to actions. For reasoning about intuitive and simple strategies, we introduce SL[F ] with natural strategies and imperfect information, denoted NatSL[F ]. ...

... Rational verification is studied in [28,29]. This problem (which is not a synthesis problem) is to decide whether a given LTL formula is satisfied by the outcome of all Nash equilibria (resp. ...