DeepAI

# Synthesis from Weighted Specifications with Partial Domains over Finite Words

In this paper, we investigate the synthesis problem of terminating reactive systems from quantitative specifications. Such systems are modeled as finite transducers whose executions are represented as finite words in (I× O)^*, where I,O are finite sets of input and output symbols, respectively. A weighted specification S assigns a rational value (or -∞) to words in (I× O)^*, and we consider three kinds of objectives for synthesis, namely threshold objectives where the system's executions are required to be above some given threshold, best-value and approximate objectives where the system is required to perform as best as it can by providing output symbols that yield the best value and ε-best value respectively w.r.t. S. We establish a landscape of decidability results for these three objectives and weighted specifications with partial domain over finite words given by deterministic weighted automata equipped with sum, discounted-sum and average measures. The resulting objectives are not regular in general and we develop an infinite game framework to solve the corresponding synthesis problems, namely the class of (weighted) critical prefix games.

• 7 publications
• 3 publications
• 3 publications
03/23/2018

### A Curry-Howard Approach to Church's Synthesis

Church's synthesis problem asks whether there exists a finite-state stre...
04/10/2018

### Coverability: Realizability Lower Bounds

We introduce the problem of temporal coverability for realizability and ...
04/13/2018

### Reactive Control Improvisation

Reactive synthesis has become a widely-used paradigm for automatically b...
05/26/2021

### TEMPEST – Synthesis Tool for Reactive Systems and Shields in Probabilistic Environments

We present Tempest, a synthesis tool to automatically create correct-by-...
08/28/2018

### Bounded Synthesis of Register Transducers

Reactive synthesis aims at automatic construction of systems from their ...
06/06/2022

### Randomized Synthesis for Diversity and Cost Constraints with Control Improvisation

In many synthesis problems, it can be essential to generate implementati...
01/03/2018

### On Periodicity Lemma for Partial Words

We investigate the function L(h,p,q), called here the threshold function...