Automatic Generation of Quality Specifications

Abstract

Abstract. The logic LTL extends LTL by quality operators. The satisfaction value of an LTL formula in a computation refines the 0/1 value of LTL formulas to a real value in [0,1]. The higher the value is, the better is the quality of the computation. The quality operator λ , for a quality constant λ ∈ [0, 1], enables the designer to prioritize different satisfaction possibilities. Formally, the satisfaction value of a subformula λ ϕ is λ times the satisfaction value of ϕ. For example, the LTL formula G(req → (Xgrant ∨ 1 2 F grant)) has value 1 in computations in which every request is immediately followed by a grant, value 1 2 if grants to some requests involve a delay, and value 0 if some request is not followed by a grant. The design of an LTL formula typically starts with an LTL formula on top of which the designer adds the parameterized operators. In the Boolean setting, the problem of automatic generation of specifications from binary-tagged computations is of great importance and is a very challenging one. Here we consider the quantitative counterpart: an LTL query is an LTL formula in which some of the quality constants are replaced by variables. Given an LTL query and a set of computations tagged by satisfaction values, the goal is to find an assignment to the variables in the query so that the obtained LTL formula has the given satisfaction values, or, if this is impossible, best approximates them. The motivation to solving LTL queries is that in practice it is easier for a designer to provide desired satisfaction values in representative computations than to come up with quality constants that capture his intuition of good and bad quality. We study the problem of solving LTL queries and show that while the problem is NP-hard, interesting fragments can be solved in polynomial time. One such fragment is the case of a single tagged computation, which we use for introducing a heuristic for the general case. The polynomial solution is based on an analysis of the search space, showing that reasoning about the infinitely many possible assignments can proceed by reasoning about their partition into finitely many classes. Our experimental results show the effectiveness and favorable outcome of the heuristic.

Automated temporal equilibrium analysis: Verification and synthesis of multi-player games

“…One might want to introduce stability, thereby making the core non-empty. One approach, which relates to the above conjecture, involves modifying the utility functions, for instance, through subsidies or rewards [41,2]. Another approach is to introduce norms [50].…”

“…We emphasise that this paper concerns the outcome of games when such agreements can be reached. The mechanism for agreements is assumed to be exogenous and beyond the scope of this paper 2. We note that linear programming and convex analysis are well-established tools for studying the core in traditional economics (see e.g.,[33,10,53,58]).…”

Alternating Reachability Games with Behavioral and Revenue Objectives

“…The formal-verification community has already adapted many concepts from classical game theory. Beyond the transition to the rational setting, researchers have studied an extension of rational synthesis to quantitative specifications [11,16], studied the stability of games with Borel winning conditions [9,7], and studied repair of rational-synthesis games, where repair amounts to making the game stable [2]. Still, the utility of a player in all these games depends only on the trace generated during the game and the level of satisfaction of her objective in this trace.…”