Synthesis from Component Libraries with Costs

Abstract

Synthesis is the automated construction of a system from its specification. In real life, hardware and software systems are rarely constructed from scratch. Rather, a system is typically constructed from a library of components. Lustig and Vardi formalized this intuition and studied LTL synthesis from component libraries. In real life, designers seek optimal systems. In this paper we add optimality considerations to the setting. We distinguish between quality considerations (for example, size -the smaller a system is, the better it is), and pricing (for example, the payment to the company who manufactured the component). We study the problem of designing systems with minimal quality-cost and price. A key point is that while the quality cost is individual -the choices of a designer are independent of choices made by other designers that use the same library, pricing gives rise to a resource-allocation game -designers that use the same component share its price, with the share being proportional to the number of uses (a component can be used several times in a design). We study both closed and open settings, and in both we solve the problem of finding an optimal design. In a setting with multiple designers, we also study the game-theoretic problems of the induced resource-allocation game.

LTL with Arithmetic and its Applications in Reasoning about Hierarchical Systems

“…While we conjecture that the problem can be solved in PSPACE, essentially by combining the nonemptiness algorithm for NBWAs with a partition of Z to equivalence classes, we think that a more practical formulation of the satisfiability problem in the context of hierarchical systems should take into an account the goal of generating succinct hierarchical systems. Thus, it should be combined with some quality measures, as in [6], which direct the algorithm to search for solutions that use the hierarchy in a meaningful way. We find this, as well as a similar extension to the synthesis problem, to be of both theoretical and practical interests.…”

Network-formation games with regular objectives

“…Since we consider long runs, the fact that the last cycle might be partial is ignored in the calculations below. Let π 1 = (C 4 ) 1 4 and…”

“…For the lower bound, we alter the reduction in [4], for the ∃NE problem in a similar game. The reduction is from the complement of the min-max vertex cover problem (MMVC, for short), which is known to P 2 -complete [25].…”

“…In the context of formal methods, an appealing application of resource-allocation games is that of synthesis from components, where the resources are components from a library, and agents need to synthesize their objectives using the components, possibly by a repeated use of some components. In some settings, the components have construction costs (e.g., the money paid to the designer of the component), in which case the corresponding multiset game is a cost-sharing game [4], and our results here can be generalized to apply for this settings. In other settings, the components have congestion effects (e.g., the components are CPUs, and the more players that use them, the slower the performance is), in which case the corresponding game is a multiset congestion game [7].…”

Alternating Reachability Games with Behavioral and Revenue Objectives

“…To the best of our knowledge, ARGTs are the first model to combine behavioral and revenue objectives. Some research on synthesis does take into account the cost of generating the synthesized system, say when the system is composed from a library of components [6], or when the system has a limited budget for sensing the environment [8] or for dealing with a dishonest environment [17]. In our model, however, the revenue is generated by payments among the players and captures dependencies among them.…”