3,505 research outputs found
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, the problem
turns out to be undecidable. 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. We prove that model-checking SLii restricted to hierarchical instances
is decidable. This result, because it allows for complex patterns of
existential and universal quantification on strategies, greatly generalises
previous ones, such as decidability of multi-player games with imperfect
information and hierarchical observations, and decidability of distributed
synthesis for hierarchical systems. To establish the decidability result, we
introduce and study QCTL*ii, an extension of QCTL* (itself an extension of CTL*
with second-order quantification over atomic propositions) by parameterising
its quantifiers with observations. The simple syntax of QCTL* ii allows us to
provide a conceptually neat reduction of SLii to QCTL*ii that separates
concerns, allowing one to forget about strategies and players and focus solely
on second-order quantification. While the model-checking problem of QCTL*ii is,
in general, undecidable, we identify a syntactic fragment of hierarchical
formulas and prove, using an automata-theoretic approach, that it is decidable.
The decidability result for SLii follows since the reduction maps hierarchical
instances of SLii to hierarchical formulas of QCTL*ii
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
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
The Complexity of Synthesizing Uniform Strategies
We investigate uniformity properties of strategies. These properties involve
sets of plays in order to express useful constraints on strategies that are not
\mu-calculus definable. Typically, we can state that a strategy is
observation-based. We propose a formal language to specify uniformity
properties, interpreted over two-player turn-based arenas equipped with a
binary relation between plays. This way, we capture e.g. games with winning
conditions expressible in epistemic temporal logic, whose underlying
equivalence relation between plays reflects the observational capabilities of
agents (for example, synchronous perfect recall). Our framework naturally
generalizes many other situations from the literature. We establish that the
problem of synthesizing strategies under uniformity constraints based on
regular binary relations between plays is non-elementary complete.Comment: In Proceedings SR 2013, arXiv:1303.007
A Backward-traversal-based Approach for Symbolic Model Checking of Uniform Strategies for Constrained Reachability
Since the introduction of Alternating-time Temporal Logic (ATL), many logics
have been proposed to reason about different strategic capabilities of the
agents of a system. In particular, some logics have been designed to reason
about the uniform memoryless strategies of such agents. These strategies are
the ones the agents can effectively play by only looking at what they observe
from the current state. ATL_ir can be seen as the core logic to reason about
such uniform strategies. Nevertheless, its model-checking problem is difficult
(it requires a polynomial number of calls to an NP oracle), and practical
algorithms to solve it appeared only recently.
This paper proposes a technique for model checking uniform memoryless
strategies. Existing techniques build the strategies from the states of
interest, such as the initial states, through a forward traversal of the
system. On the other hand, the proposed approach builds the winning strategies
from the target states through a backward traversal, making sure that only
uniform strategies are explored. Nevertheless, building the strategies from the
ground up limits its applicability to constrained reachability objectives only.
This paper describes the approach in details and compares it experimentally
with existing approaches implemented into a BDD-based framework. These
experiments show that the technique is competitive on the cases it can handle.Comment: In Proceedings GandALF 2017, arXiv:1709.0176
ATLsc with partial observation
Alternating-time temporal logic with strategy contexts (ATLsc) is a powerful
formalism for expressing properties of multi-agent systems: it extends CTL with
strategy quantifiers, offering a convenient way of expressing both
collaboration and antagonism between several agents. Incomplete observation of
the state space is a desirable feature in such a framework, but it quickly
leads to undecidable verification problems. In this paper, we prove that
uniform incomplete observation (where all players have the same observation)
preserves decidability of the model-checking problem, even for very expressive
logics such as ATLsc.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
New results on pushdown module checking with imperfect information
Model checking of open pushdown systems (OPD) w.r.t. standard branching
temporal logics (pushdown module checking or PMC) has been recently
investigated in the literature, both in the context of environments with
perfect and imperfect information about the system (in the last case, the
environment has only a partial view of the system's control states and stack
content). For standard CTL, PMC with imperfect information is known to be
undecidable. If the stack content is assumed to be visible, then the problem is
decidable and 2EXPTIME-complete (matching the complexity of PMC with perfect
information against CTL). The decidability status of PMC with imperfect
information against CTL restricted to the case where the depth of the stack
content is visible is open. In this paper, we show that with this restriction,
PMC with imperfect information against CTL remains undecidable. On the other
hand, we individuate an interesting subclass of OPDS with visible stack content
depth such that PMC with imperfect information against the existential fragment
of CTL is decidable and in 2EXPTIME. Moreover, we show that the program
complexity of PMC with imperfect information and visible stack content against
CTL is 2EXPTIME-complete (hence, exponentially harder than the program
complexity of PMC with perfect information, which is known to be
EXPTIME-complete).Comment: In Proceedings GandALF 2011, arXiv:1106.081
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