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Program verification and synthesis frameworks that allow one to customize the language in which one is interested typically require the user to provide a formally defined semantics for the language. Because writing a formal semantics can be a daunting and error-prone task, this requirement stands in the way of such frameworks being adopted by non-expert users. We present an algorithm that can automatically synthesize inductively defined syntax-directed semantics when given (i) a grammar describing the syntax of a language and (ii) an executable (closed-box) interpreter for computing the semantics of programs in the language of the grammar. Our algorithm synthesizes the semantics in the form of Constrained-Horn Clauses (CHCs), a natural, extensible, and formal logical framework for specifying inductively defined relations that has recently received widespread adoption in program verification and synthesis. The key innovation of our synthesis algorithm is a Counterexample-Guided Synthesis (CEGIS) approach that breaks the hard problem of synthesizing a set of constrained Horn clauses into small, tractable expression-synthesis problems that can be dispatched to existing SyGuS synthesizers. Our tool Synantic synthesized inductively-defined formal semantics from 14 interpreters for languages used in program-synthesis applications. When synthesizing formal semantics for one of our benchmarks, Synantic unveiled an inconsistency in the semantics computed by the interpreter for a language of regular expressions; fixing the inconsistency resulted in a more efficient semantics and, for some cases, in a 1.2x speedup for a synthesizer solving synthesis problems over such a language. 

Program sketching is a program synthesis paradigm in which the programmer provides a partial program with holes and assertions. The goal of the synthesizer is to automatically find integer values for the holes so that the resulting program satisfies the assertions. The most popular sketching tool, Sketch , can efficiently solve complex program sketches but uses an integer encoding that often performs poorly if the sketched program manipulates large integer values. In this article, we propose a new solving technique that allows Sketch to handle large integer values while retaining its integer encoding. Our technique uses a result from number theory, the Chinese Remainder Theorem, to rewrite program sketches to only track the remainders of certain variable values with respect to several prime numbers. We prove that our transformation is sound and the encoding of the resulting programs are exponentially more succinct than existing Sketch encodings. We evaluate our technique on a variety of benchmarks manipulating large integer values. Our technique provides speedups against both existing Sketch solvers and can solve benchmarks that existing Sketch solvers cannot handle. 

This paper addresses the problem of creating abstract transformers automatically. The method we present automates the construction of static analyzers in a fashion similar to the wayyaccautomates the construction of parsers. Our method treats the problem as a program-synthesis problem. The user provides specifications of (i) the concrete semantics of a given operationop, (ii) the abstract domainAto be used by the analyzer, and (iii) the semantics of a domain-specific languageLin which the abstract transformer is to be expressed. As output, our method creates an abstract transformer foropin abstract domainA, expressed inL(an “L-transformer foropoverA”). Moreover, the abstract transformer obtained is a most-preciseL-transformer foropoverA; that is, there is no otherL-transformer foropoverAthat is strictly more precise. We implemented our method in a tool called AMURTH. We used AMURTH to create sets of replacement abstract transformers for those used in two existing analyzers, and obtained essentially identical performance. However, when we compared the existing transformers with the transformers obtained using AMURTH, we discovered that four of the existing transformers were unsound, which demonstrates the risk of using manually created transformers. 

Computer science class enrollments have rapidly risen in the past decade. With current class sizes, standard approaches to grading and providing personalized feedback are no longer possible and new techniques become both feasible and necessary. In this paper, we present the third version of Automata Tutor, a tool for helping teachers and students in large courses on automata and formal languages. The second version of Automata Tutor supported automatic grading and feedback for finite-automata constructions and has already been used by thousands of users in dozens of countries. This new version of Automata Tutor supports automated grading and feedback generation for a greatly extended variety of new problems, including problems that ask students to create regular expressions, context-free grammars, pushdown automata and Turing machines corresponding to a given description, and problems about converting between equivalent models - e.g., from regular expressions to nondeterministic finite automata. Moreover, for several problems, this new version also enables teachers and students to automatically generate new problem instances. We also present the results of a survey run on a class of 950 students, which shows very positive results about the usability and usefulness of the tool.