Parameterized Model Checking of Token-Passing Systems

We revisit the parameterized model checking problem for token-passing systems and specifications in indexed $\textsf{CTL}^\ast \backslash \textsf{X}$. Emerson and Namjoshi (1995, 2003) have shown that parameterized model checking of indexed $\textsf{CTL}^\ast \backslash \textsf{X}$ in uni-directional token rings can be reduced to checking rings up to some \emph{cutoff} size. Clarke et al. (2004) have shown a similar result for general topologies and indexed $\textsf{LTL} \backslash \textsf{X}$, provided processes cannot choose the directions for sending or receiving the token. We unify and substantially extend these results by systematically exploring fragments of indexed $\textsf{CTL}^\ast \backslash \textsf{X}$ with respect to general topologies. For each fragment we establish whether a cutoff exists, and for some concrete topologies, such as rings, cliques and stars, we infer small cutoffs. Finally, we show that the problem becomes undecidable, and thus no cutoffs exist, if processes are allowed to choose the directions in which they send or from which they receive the token.Comment: We had to remove an appendix until the proofs and notations there is cleare

EPTCS

First cycle games (FCG) are played on a finite graph by two players who push a token along the edges until a vertex is repeated, and a simple cycle is formed. The winner is determined by some fixed property Y of the sequence of labels of the edges (or nodes) forming this cycle. These games are traditionally of interest because of their connection with infinite-duration games such as parity and mean-payoff games. We study the memory requirements for winning strategies of FCGs and certain associated infinite duration games. We exhibit a simple FCG that is not memoryless determined (this corrects a mistake in Memoryless determinacy of parity and mean payoff games: a simple proof by Bj⋯orklund, Sandberg, Vorobyov (2004) that claims that FCGs for which Y is closed under cyclic permutations are memoryless determined). We show that θ (n)! memory (where n is the number of nodes in the graph), which is always sufficient, may be necessary to win some FCGs. On the other hand, we identify easy to check conditions on Y (i.e., Y is closed under cyclic permutations, and both Y and its complement are closed under concatenation) that are sufficient to ensure that the corresponding FCGs and their associated infinite duration games are memoryless determined. We demonstrate that many games considered in the literature, such as mean-payoff, parity, energy, etc., satisfy these conditions. On the complexity side, we show (for efficiently computable Y) that while solving FCGs is in PSPACE, solving some families of FCGs is PSPACE-hard

Stochastic Fairness and Language-Theoretic Fairness in Planning in Nondeterministic Domains

We address two central notions of fairness in the literature of nondeterministic fully observable domains. The first, which we call stochastic fairness, is classical, and assumes an environment which operates probabilistically using possibly unknown probabilities. The second, which is language-theoretic, assumes that if an action is taken from a given state infinitely often then all its possible outcomes should appear infinitely often; we call this state-action fairness. While the two notions coincide for standard reachability goals, they differ for temporally extended goals. This important difference has been overlooked in the planning literature and has led to the use of a product-based reduction in a number of published algorithms which were stated for state-action fairness, for which they are incorrect, while being correct for stochastic fairness. We remedy this and provide a correct optimal algorithm for solving state-action fair planning for LTL/LTLf goals, as well as a correct proof of the lower bound of the goal-complexity. Our proof is general enough that it also pro- vides, for the no-fairness and stochastic-fairness cases, multiple missing lower bounds and new proofs of known lower bounds. Overall, we show that stochastic fairness is better behaved than state-action fairness

Synthesizing strategies under expected and exceptional environment behaviors

We consider an agent that operates with two models of the environment: one that captures expected behaviors and one that captures additional exceptional behaviors. We study the problem of synthesizing agent strategies that enforce a goal against environments operating as expected while also making a best effort against exceptional environment behaviors. We formalize these concepts in the context of linear-temporal logic, and give an algorithm for solving this problem. We also show that there is no trade-off between enforcing the goal under the expected environment specification and making a best-effort for it under the exceptional one

Model Checking Parameterised Multi-token Systems via the Composition Method

The final publication is available via https://doi.org/10.1007/978-3-319-40229-1_34.We study the model checking problem of parameterised systems with an arbitrary number of processes, on arbitrary network-graphs, communicating using multiple multi-valued tokens, and specifications from indexed-branching temporal logic. We prove a composition theorem, in the spirit of Feferman-Vaught [21] and Shelah [31], and a finiteness theorem, and use these to decide the model checking problem. Our results assume two constraints on the process templates, one of which is the standard fairness assumption introduced in the cornerstone paper of Emerson and Namjoshi [18]. We prove that lifting any of these constraints results in undecidability. The importance of our work is three-fold: (i) it demonstrates that the composition method can be fruitfully applied to model checking complex parameterised systems; (ii) it identifies the most powerful model, to date, of parameterised systems for which model checking indexed branching-time specifications is decidable; (iii) it tightly marks the borders of decidability of this model.Vienna Science Fund (WWTF