Related papers: What's hard about Boolean Functional Synthesis
Automatic synthesis of hardware components from declarative specifications is an ambitious endeavor in computer aided design. Existing synthesis algorithms are often implemented with Binary Decision Diagrams (BDDs), inheriting their…
A modern approach to engineering correct-by-construction systems is to synthesize them automatically from formal specifications. Oftentimes, a system can only satisfy its guarantees if certain environment assumptions hold, which motivates…
We consider the task of program synthesis in the presence of a reward function over the output of programs, where the goal is to find programs with maximal rewards. We employ an iterative optimization scheme, where we train an RNN on a…
A Boolean function of n bits is balanced if it takes the value 1 with probability 1/2. We exhibit a balanced Boolean function with a randomized evaluation procedure (with probability 0 of making a mistake) so that on uniformly random…
In the past few years, Large Language Models (LLMs) have exploded in usefulness and popularity for code generation tasks. However, LLMs still struggle with accuracy and are unsuitable for high-risk applications without additional oversight…
A quantum single-error-correcting scheme can be derived from a one-way entanglement purification protocol in purifying one Bell state from a finite block of five Bell states. The main issue to be concerned with in the theory of such an…
Developing critical components, such as mission controllers or embedded systems, is a challenging task. Reactive synthesis is a technique to automatically produce correct controllers. Given a high-level specification written in LTL,…
Inspired by recent progress in dynamic programming approaches for weighted model counting, we investigate a dynamic-programming approach in the context of boolean realizability and synthesis, which takes a conjunctive-normal-form boolean…
Program synthesis is the task of constructing a program conforming to a given specification. We focus on deductive synthesis, and in particular on synthesis problems with specifications given as $\forall\exists$-formulas, expressing the…
This work introduces efficient symbolic algorithms for quantitative reactive synthesis. We consider resource-constrained robotic manipulators that need to interact with a human to achieve a complex task expressed in linear temporal logic.…
Given a Linear Temporal Logic (LTL) formula over input and output variables, reactive synthesis requires us to design a deterministic Mealy machine that gives the values of outputs at every time step for every sequence of inputs, such that…
Invariants are key to formal loop verification as they capture loop properties that are valid before and after each loop iteration. Yet, generating invariants is a notorious task already for syntactically restricted classes of loops. Rather…
Program Synthesis is the mapping of a specification of what a computer program is supposed to do, into a computer program that does what the specification says to do. This is equivalent to constructing any computer program and a sound proof…
We say that a function is rare-case hard against a given class of algorithms (the adversary) if all algorithms in the class can compute the function only on an $o(1)$-fraction of instances of size $n$ for large enough $n$. Starting from any…
Program synthesis is a class of regression problems where one seeks a solution, in the form of a source-code program, mapping the inputs to their corresponding outputs exactly. Due to its precise and combinatorial nature, program synthesis…
Boolean operations are among the most used paradigms to create and edit digital shapes. Despite being conceptually simple, the computation of mesh Booleans is notoriously challenging. Main issues come from numerical approximations that make…
With the proliferation of increasingly complicated Deep Learning architectures, data synthesis is a highly promising technique to address the demand of data-hungry models. However, reliably assessing the quality of a 'synthesiser' model's…
In this paper, we study incremental LTLf synthesis -- a form of reactive synthesis where the goals are given incrementally while in execution. In other words, the protagonist agent is already executing a strategy for a certain goal when it…
In this paper an algorithm is designed which generates in-equivalent Boolean functions of any number of variables from the four Boolean functions of single variable. The grammar for such set of Boolean function is provided. The Turing…
It is believed that there is no efficient classical algorithm to determine the linear structure of Boolean function. We investigate an extension of Simon's period-finding quantum algorithm, and propose an efficient quantum algorithm to…