Weighted Strategy Logic with Boolean Goals Over One-Counter Games

Strategy Logic is a powerful specification language for expressing non-zero-sum properties of multi-player games. SL conveniently extends the logic ATL with explicit quantification and assignment of strategies. In this paper, we consider games over one-counter automata, and a quantitative extension 1cSL of SL with assertions over the value of the counter. We prove two results: we first show that, if decidable, model checking the so-called Boolean-goal fragment of 1cSL has non-elementary complexity; we actually prove the result for the Boolean-goal fragment of SL over finite-state games, which was an open question in [Mogavero et al. Reasoning about strategies: On the model-checking problem. ACM ToCL 15(4),2014]. As a first step towards proving decidability, we then show that the Boolean-goal fragment of 1cSL over one-counter games enjoys a nice periodicity property

Dependences in Strategy Logic

Strategy Logic (SL) is a very expressive temporal logic for specifying and verifying properties of multi-agent systems: in SL, one can quantify over strategies, assign them to agents, and express LTL properties of the resulting plays. Such a powerful framework has two drawbacks: First, model checking SL has non-elementary complexity; second, the exact semantics of SL is rather intricate, and may not correspond to what is expected. In this paper, we focus on strategy dependences in SL, by tracking how existentially-quantified strategies in a formula may (or may not) depend on other strategies selected in the formula, revisiting the approach of [Mogavero et al., Reasoning about strategies: On the model-checking problem, 2014]. We explain why elementary dependences, as defined by Mogavero et al., do not exactly capture the intended concept of behavioral strategies. We address this discrepancy by introducing timeline dependences, and exhibit a large fragment of SL for which model checking can be performed in 2-EXPTIME under this new semantics

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