Related papers: Completeness of Synthesis under Realizability Assu…

Proof by coupling is a classical technique for proving properties about pairs of randomized algorithms by carefully relating (or coupling) two probabilistic executions. In this paper, we show how to automatically construct such proofs for…

We develop an approach to estimate the probability that a program sampled from a large language model is correct. Given a natural language description of a programming problem, our method samples both candidate programs as well as candidate…

Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…

We present a computer-aided programming approach to concurrency. The approach allows programmers to program assuming a friendly, non-preemptive scheduler, and our synthesis procedure inserts synchronization to ensure that the final program…

Probabilistic programs are key to deal with uncertainty in e.g. controller synthesis. They are typically small but intricate. Their development is complex and error prone requiring quantitative reasoning over a myriad of alternative…

Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the…

This paper presents a method for synthesising sound and complete tableau calculi. Given a specification of the formal semantics of a logic, the method generates a set of tableau inference rules that can then be used to reason within the…

Conjecturing and theorem proving are activities at the center of mathematical practice and are difficult to separate. In this paper, we propose a framework for completing incomplete conjectures and incomplete proofs. The framework can turn…

Synthesis is the automatic construction of a system from its specification. In classical synthesis algorithms it is always assumed that the system is "constructed from scratch" rather than composed from reusable components. This, of course,…

We present a tractable method for synthesizing arbitrarily large concurrent programs, for a shared memory model with common hardware-available primitives such as atomic registers, compare-and-swap, load-linked/store conditional, etc. The…

Automatic software generation based on some specification is known as program synthesis. Most existing approaches formulate program synthesis as a search problem with discrete parameters. In this paper, we present a novel formulation of…

Synthesizing programs from examples requires searching over a vast, combinatorial space of possible programs. In this search process, a key challenge is representing the behavior of a partially written program before it can be executed, to…

This abstract extends on the previous work (arXiv:1407.2646, arXiv:1606.00075) on program induction using probabilistic programming. It describes possible further steps to extend that work, such that, ultimately, automatic probabilistic…

We present an incomplete proof synthesis method for the Calculus of Constructions which is always terminating and a complete Vernacular for the Calculus of Constructions based on this method.

Essential tasks for the verification of probabilistic programs include bounding expected outcomes and proving termination in finite expected runtime. We contribute a simple yet effective inductive synthesis approach for proving such…

This paper presents an example of formal reasoning about the semantics of a Prolog program of practical importance (the SAT solver of Howe and King). The program is treated as a definite clause logic program with added control. The logic…

It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…

Proving equivalence between functional programs is a fundamental problem in program verification, which often amounts to reasoning about algebraic data types (ADTs) and compositions of structural recursions. Modern theorem provers address…

Our research concerns generating imperative programs from Answer Set Programming Specifications. ASP is highly declarative and is ideal for writing specifications. Further with negation-as-failure it is easy to succinctly represent…

Program completion is a translation from the language of logic programs into the language of first-order theories. Its original definition has been extended to programs that include integer arithmetic, accept input, and distinguish between…