14 research outputs found
Relentful Strategic Reasoning in 1 Alternating-Time Temporal Logic
Temporal logics are a well investigated formalism for the specification, verification, and synthesis of reactive systems.
Within this family, Alternating-Time Temporal Logic (ATL , for short) has been introduced as a useful generalization
of classical linear- and branching-time temporal logics, by allowing temporal operators to be indexed by coalitions of
agents. Classically, temporal logics are memoryless: once a path in the computation tree is quantified at a given node,
the computation that has led to that node is forgotten. Recently, mCTL has been defined as a memoryful variant
of CTL , where path quantification is memoryful. In the context of multi-agent planning, memoryful quantification
enables agents to “relent” and change their goals and strategies depending on their history.
In this paper, we define mATL , a memoryful extension of ATL , in which a formula is satisfied at a certain
node of a path by taking into account both the future and the past. We study the expressive power of mATL ,
its succinctness, as well as related decision problems. We also investigate the relationship between memoryful
quantification and past modalities and show their equivalence. We show that both the memoryful and the past
extensions come without any computational price; indeed, we prove that both the satisfiability and the model-checking
problems are 2EXPTIME-COMPLETE, as they are for AT
Satisfiability in Strategy Logic can be Easier than Model Checking
In the design of complex systems, model-checking and satisfiability arise as two prominent decision problems. While model-checking requires the designed system to be provided in advance, satisfiability allows to check if such a system even exists. With very few exceptions, the second problem turns out to be harder than the first one from a complexity-theoretic standpoint. In this paper, we investigate the connection between the two problems for a non-trivial fragment of Strategy Logic (SL, for short). SL extends LTL with first-order quantifications over strategies, thus allowing to explicitly reason about the strategic abilities of agents in a multi-agent system. Satisfiability for the full logic is known to be highly undecidable, while model-checking is non-elementary.The SL fragment we consider is obtained by preventing strategic quantifications within the scope of temporal operators. The resulting logic is quite powerful, still allowing to express important game-theoretic properties of multi-agent systems, such as existence of Nash and immune equilibria, as well as to formalize the rational synthesis problem. We show that satisfiability for such a fragment is PSPACE-COMPLETE, while its model-checking complexity is 2EXPTIME-HARD. The result is obtained by means of an elegant encoding of the problem into the satisfiability of conjunctive-binding first-order logic, a recently discovered decidable fragment of first-order logic
Results on Alternating-Time Temporal Logics with Linear Past
We investigate the succinctness gap between two known equally-expressive and different linear-past extensions of standard CTL^* (resp., ATL^*). We establish by formal non-trivial arguments that the "memoryful" linear-past extension (the history leading to the current state is taken into account) can be exponentially more succinct than the standard "local" linear-past extension (the history leading to the current state is forgotten). As a second contribution, we consider the ATL-like fragment, denoted ATL_{lp}, of the known "memoryful" linear-past extension of ATL^{*}. We show that ATL_{lp} is strictly more expressive than ATL, and interestingly, it can be exponentially more succinct than the more expressive logic ATL^{*}. Moreover, we prove that both satisfiability and model-checking for the logic ATL_{lp} are Exptime-complete
Reasoning About Strategies: On the Model-Checking Problem
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, such as ATL, ATL\star, and the like.
Recently, Chatterjee, Henzinger, and Piterman introduced Strategy Logic, which
we denote here by CHP-SL, with the aim of getting a powerful framework for
reasoning explicitly about strategies. CHP-SL is obtained by using first-order
quantifications over strategies and has been investigated in the very specific
setting of two-agents turned-based games, where a non-elementary model-checking
algorithm has been provided. While CHP-SL is a very expressive logic, we claim
that it does not fully capture the strategic aspects of multi-agent systems. In
this paper, we introduce and study a more general strategy logic, denoted SL,
for reasoning about strategies in multi-agent concurrent games. We prove that
SL includes CHP-SL, while maintaining a decidable model-checking problem. In
particular, the algorithm we propose is computationally not harder than the
best one known for CHP-SL. Moreover, we prove that such a problem for SL is
NonElementarySpace-hard. This negative result has spurred us to investigate
here syntactic fragments of SL, strictly subsuming ATL\star, with the hope of
obtaining an elementary model-checking problem. Among the others, we study the
sublogics SL[NG], SL[BG], and SL[1G]. They encompass formulas in a special
prenex normal form having, respectively, nested temporal goals, Boolean
combinations of goals and, a single goal at a time. About these logics, we
prove that the model-checking problem for SL[1G] is 2ExpTime-complete, thus not
harder than the one for ATL\star
Parity-energy ATL for Qualitative and Quantitative Reasoning in MAS
In this paper, we introduce a new logic suitable to reason about strategic
abilities of multi-agent systems where (teams of) agents are subject to
qualitative (parity) and quantitative (energy) constraints and where goals are
represented, as usual, by means of temporal properties.
We formally define such a logic, named parity-energy-atl (peatl, for short),
and we study its model checking problem, which we prove to be decidable with
different complexity upper bounds, depending on different choices for the
energy range
Taming Strategy Logic: Non-Recurrent Fragments
Strategy Logic ([Formula presented] for short) is one of the prominent languages for reasoning about the strategic abilities of agents in a multi-agent setting. This logic extends [Formula presented] with first-order quantifiers over the agent strategies and encompasses other formalisms, such as [Formula presented] and [Formula presented]. The model-checking problem for [Formula presented] and several of its fragments has been extensively studied. On the other hand, the picture is much less clear on the satisfiability front, where the problem is undecidable for the full logic. In this work, we study two fragments of One-Goal [Formula presented], where the nesting of sentences within temporal operators is constrained. We show that the satisfiability problem for these two logics, and for the corresponding fragments of [Formula presented] and [Formula presented], is in [Formula presented] and [Formula presented], respectively
Multi-agent Path Planning in Known Dynamic Environments
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 (called the arena) while the dynamic environment is treated as just another agent. The complexity of planning using this representation is pspace-complete. The arena complexity (i.e., the complexity of the planning problem in which the graph is the only input, in particular, the number of agents is fixed) is np-hard. Thus, we provide structural restrictions that put the arena complexity of the planning problem into ptime(for any fixed number of agents). The importance of our work is that these structural conditions (and hence the complexity results) do not depend on graph-theoretic properties of the arena (such as clique- or tree-width), but rather on the abilities of the agents
Strategic Reasoning in Game Theory
Game theory in AI is a powerful mathematical framework largely applied in the last three decades for the strategic reasoning in multi-agent systems. Seminal works along this line started with turn-based two-player games (under perfect and imperfect information) to check the correctness of a system against an unpredictable environment. Then, large effort has been devoted to extend those works to the multi-agent setting and, specifically, to efficiently reasoning about important solution concepts such as Nash Equilibria and the like. Breakthrough contributions along this direction concern the introduction of logics for the strategic reasoning such as Alternating-time Temporal Logic (ATL), Strategy Logic (SL), and their extensions.
Two-player games and logics for the strategic reasoning are nowadays very active areas of research. In this thesis we significantly advance the work along both these two lines of research by providing fresh studies and results of practical application.
We start with two-player reachability games and first investigate the problem of checking whether a designed player has more than a winning strategy to reach a target. We investigate this question under both perfect and imperfect information. We provide an automata-based solution that requires linear-time, in the perfect information setting, and exponential-time, in the imperfect one. In both cases, the results are tight. Then, we move to multi-player concurrent games and study the following specific setting: (i) Player_0's objective is to reach a target W, and (ii) the opponents are trying to stop this but have partial observation about Player_0's actions. We study the problem of deciding whether the opponents can prevent Player_0 to reach W. We show, using an automata-theoretic approach that, assuming the opponents have the same partial observation and play under uniformity, the problem is in ExpTime. We recall that, in general, multi-player reachability games with imperfect information are undecidable.
Then, we move to the more expressive framework of logics for the strategic reasoning. We first introduce and study two graded extensions of SL, namely GSL and GradedSL. By the former, we define a graded version over single strategy variables, i.e. "there exist at least g different strategies", where the strategies are counted semantically. We study the model checking-problem for GSL and show that for its fragment called vanilla GSL[1G] the problem is PTime-complete. By GradedSL, we consider a graded version over tuple of strategy variables and use a syntactic counting over strategies. By means of GradedSL we show how to count the number of different strategy profiles that are Nash equilibria (NE). By analyzing the structure of the specific formulas involved, we conclude that the important problem of checking for the existence of a unique NE can be solved in 2ExpTime, which is not harder than merely checking for the existence of such an equilibrium.
Finally, we adopt the view of bounded rationality, and look only at "simple" strategies in specifications of agents’ abilities. We formally define what "simple" means, and propose a variant of plain ATL, namely NatATL, that takes only such strategies into account. We study the model checking problem for the resulting semantics of ability and obtain tight results. The positive results achieved with NatATL encourage for the investigation of simple strategies over more powerful logics, including SL