Parametric Interval Temporal Logic over Infinite Words

Model checking for Halpern and Shoham’s interval temporal logic HS has been recently investigated in a systematic way, and it is known to be decidable under three distinct semantics. Here, we focus on the trace-based semantics, where the infinite execution paths (traces) of the given (finite) Kripke structure are the main semantic entities. In this setting, each finite infix of a trace is interpreted as an interval, and a proposition holds over an interval if and only if it holds over each component state (homogeneity assumption). In this paper, we introduce a quantitative extension of HS over traces, called parametric HS (PHS). The novel logic allows to express parametric timing constraints on the duration (length) of the intervals. We show that checking the existence of a parameter valuation for which a Kripke structure satisfies a PHS formula (model checking), or a PHS formula admits a trace as a model under the homogeneity assumption (satisfiability) is decidable. Moreover, we identify a fragment of PHS which subsumes parametric LTL and for which model checking and satisfiability are shown to be EXPSPACE-complete

Complexity and succinctness issues for linear-time hybrid logics

Full linear-time hybrid logic (HL) is a non-elementary and equally expressive extension of standard LTL C past obtained by adding the well-known binder operators. We investigate complexity and succinctness issues for HL in terms of the number of variables and nesting depth of binder modalities. First,wepresent direct automata-theoretic decision procedures for satisfiability and model-checking of HL, which require space of exponential height equal to the nesting depth of the binder modalities. The proposed algorithms are proved to be asymptotically optimal by providing matching lower bounds. Second, we show that, for the one-variable fragment of HL, the considered problems are elementary and, precisely, Expspace-complete. Finally, we show that, for all 0 <= h < k, there is a succinctness gap between the fragments HL^k and HL^h with binder nesting depth at most k and h, respectively, of exponential height equal to

An Epistemic Strategy Logic

This article presents an extension of temporal epistemic logic with operators that can express quantification over agent strategies. Unlike previous work on alternating temporal epistemic logic, the semantics works with systems whose states explicitly encode the strategy being used by each of the agents. This provides a natural way to express what agents would know were they to be aware of some of the strategies being used by other agents. A number of examples that rely on the ability to express an agent’s knowledge about the strategies being used by other agents are presented to motivate the framework, including reasoning about game-theoretic equilibria, knowledge-based programs, and information-theoretic computer security policies. Relationships to several variants of alternating temporal epistemic logic are discussed. The computational complexity of model checking the logic and several of its fragments are also characterized

Complexity and Succinctness issues for linear-time hybrid logics

Full linear-time hybrid logic (HL) is a non-elementary and equally expressive extension of standard LTL + past obtained by adding the well-known binder operators ↓ and ∃. We investigate complexity and succinctness issues for HL in terms of the number of variables and nesting depth of binder modalities. First, we present direct automata-theoretic decision procedures for satisfiability and model-checking of HL, which require space of exponential height equal to the nesting depth of binder modalities. The proposed algorithms are proved to be asymptotically optimal by providing matching lower bounds. Second, we show that for the one-variable fragment of HL, the considered problems are elementary and, precisely, EXPSPACE-complete. Finally, we show that for all 0 ≤ h &lt; k,there is a succinctness gap between the fragments HL k and HL h with binder nesting depth at most k and h, respectively, of exponential height equal to k − h