We introduce RFixer, a tool for repairing complex regular expressions using examples. Given an incorrect regular expression and sets of positive and negative examples, RFixer synthesizes the closest regular expression to the original one that is consistent with the examples. Automatically repairing regular expressions requires exploring a large search space because practical regular expressions: i) are large, ii) operate over very large alphabetsÐe.g., UTF-16 and ASCIIÐand iii) employ complex constructsÐe.g., character classes and numerical quantifiers. RFixer's repair algorithm achieves scalability by taking advantage of structural properties of regular expressions to effectively prune the search space, and it employs satisfiability modulo theory solvers to efficiently and symbolically explore the sets of possible character classes and numerical quantifiers. RFixer could successfully compute minimal repairs for regular expressions collected from a variety of sources, whereas existing tools either failed to produce any repair or produced overly complex repairs. CCS Concepts: • Software and its engineering → General programming languages; • Theory of computation → Regular languages.

Abstract. Automatic program synthesis promises to increase the productivity of programmers and end-users of computing devices by automating tedious and error-prone tasks. Despite the practical successes of program synthesis, we still do not have systematic frameworks to synthesize programs that are "good" according to certain metricse.g., produce programs of reasonable sizes or with good runtime-and to understand when synthesis can result in such good programs. In this paper, we propose QSyGuS, a unifying framework for describing syntaxguided synthesis problems with quantitative objectives over the syntax of the synthesized programs. QSyGuS builds on weighted (tree) grammars, a clean and foundational formalism that provides flexible support for different quantitative objectives, useful closure properties, and practical decision procedures. We then present an algorithm for solving QSyGuS. Our algorithm leverages closure properties of weighted grammars to generate intermediate problems that can be solved using non-quantitative SyGuS solvers. Finally, we implement our algorithm in a tool, QuaSi, and evaluate it on 26 quantitative extensions of existing SyGuS benchmarks. QuaSi can synthesize optimal solutions in 15/26 benchmarks with times comparable to those needed to find an arbitrary solution.

We consider the problem of automatically establishing that a given syntax-guided-synthesis (SyGuS) problem is unrealizable (i.e., has no solution). Existing techniques have quite limited ability to establish unrealizability for general SyGuS instances in which the grammar describing the search space contains infinitely many programs. By encoding the synthesis problem's grammar G as a nondeterministic program PG, we reduce the unrealizability problem to a reachability problem such that, if a standard program-analysis tool can establish that a certain assertion in PG always holds, then the synthesis problem is unrealizable.Our method can be used to augment existing SyGuS tools so that they can establish that a successfully synthesized program q is optimal with respect to some syntactic cost-e.g., q has the fewest possible if-thenelse operators. Using known techniques, grammar G can be transformed to generate the set of all programs with lower costs than q-e.g., fewer conditional expressions. Our algorithm can then be applied to show that the resulting synthesis problem is unrealizable. We implemented the proposed technique in a tool called nope. nope can prove unrealizability for 59/132 variants of existing linear-integer-arithmetic SyGuS benchmarks, whereas all existing SyGuS solvers lack the ability to prove that these benchmarks are unrealizable, and time out on them.1 Grammar G2 only generates terms that are equivalent to some linear function of x and y; however, the maximum function cannot be described by a linear function. 2 The synthesis problem presented above is one that is generated by a recent tool called QSyGuS, which extends SyGuS with quantitative syntactic objectives [10]. The advantage of using quantitative objectives in synthesis is that they can be used to produce higher-quality solutions-e.g., smaller, more readable, more efficient, etc. The synthesis problem (ψmax2(f, x, y), G2) arises from a QSyGuS problem in which the goal is to produce an expression that (i) satisfies the specification ψmax2(f, x, y), and (ii) uses the smallest possible number of if-then-else operators. Existing SyGuS solvers can easily produce a solution that uses one if-then-else operator, but cannot prove that no better solution exists-i.e., (ψmax2(f, x, y), G2) is unrealizable.

No abstract

No abstract

Entanglement in angular momentum degrees of freedom is a precious resource for quantum metrology and control. Here we study the conversions of this resource, focusing on Bell pairs of spin-J particles, where one particle is used to probe unknown rotations and the other particle is used as reference. When a large number of pairs are given, we show that every rotated spin-J Bell state can be reversibly converted into an equivalent number of rotated spin one-half Bell states, at a rate determined by the quantum Fisher information. This result provides the foundation for the definition of an elementary unit of information about rotations in space, which we call the Cartesian refbit. In the finite copy scenario, we design machines that approximately break down Bell states of higher spins into Cartesian refbits, as well as machines that approximately implement the inverse process. In addition, we establish a quantitative link between the conversion of Bell states and the simulation of unitary gates, showing that the fidelity of probabilistic state conversion provides upper and lower bounds on the fidelity of deterministic gate simulation. The result holds not only for rotation gates, but also to all sets of gates that form finite-dimensional representations of compact groups. For rotation gates, we show how rotations on a system of given spin can simulate rotations on a system of different spin.

This paper develops a new framework for program synthesis, called semantics-guided synthesis (SemGuS), that allows a user to provide both the syntax and the semantics for the constructs in the language. SemGuS accepts a recursively defined big-step semantics, which allows it, for example, to be used to specify and solve synthesis problems over an imperative programming language that may contain loops with unbounded behavior. The customizable nature of SemGuS also allows synthesis problems to be defined over a non-standard semantics, such as an abstract semantics. In addition to the SemGuS framework, we develop an algorithm for solving SemGuS problems that is capable of both synthesizing programs and proving unrealizability, by encoding a SemGuS problem as a proof search over Constrained Horn Clauses: in particular, our approach is the first that we are aware of that can prove unrealizabilty for synthesis problems that involve imperative programs with unbounded loops, over an infinite syntactic search space. We implemented the technique in a tool called MESSY, and applied it to SyGuS problems (i.e., over expressions), synthesis problems over an imperative programming language, and synthesis problems over regular expressions.

We propose a fully-automated technique for inverting functional programs that operate over lists such as string encoders and decoders. We consider programs that can be modeled using symbolic extended finite transducers (), an expressive model that can describe complex list-manipulating programs while retaining several decidable properties. Concretely, given a program P expressed as an , we propose techniques for: (1) checking whether P is injective and, if that is the case, (2) building an P -1 describing its inverse. We first show that it is undecidable to check whether an is injective and propose an algorithm for checking injectivity for a restricted, but a practical class of . We then propose an algorithm for inverting based on the following idea: if an is injective, inverting it amounts to inverting all its individual transitions. We leverage recent advances program synthesis and show that the transition inversion problem can be expressed as an instance of the syntax-guided synthesis framework. Finally, we implement the proposed techniques in a tool called and show that can invert 13 out 14 real complex string encoders and decoders, producing inverse programs that are substantially identical to manually written ones.