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Parameter-Efficient Fine-Tuning (PEFT) has become the standard for customising Foundation Models (FMs) to user-specific downstream tasks. However, typical PEFT methods require storing multiple task-specific adapters, creating scalability issues as these adapters must be housed and run at the FM server. Traditional prompt tuning offers a potential solution by customising them through task-specific input prefixes, but it under-performs compared to other PEFT methods like LoRA. To address this gap, we propose Low-Rank Prompt Adaptation (LoPA), a prompttuning-based approach that performs on par with state-of-the-art PEFT methods and full fine-tuning while being more parameter-efficient and not requiring a server-based adapter. LoPA generates soft prompts by balancing between sharing task-specific information across instances and customization for each instance. It uses a low-rank decomposition of the soft-prompt component encoded for each instance to achieve parameter efficiency. We provide a comprehensive evaluation on multiple natural language understanding and code generation and understanding tasks across a wide range of foundation models with varying sizes. 

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. 

We consider the problem of establishing that a program-synthesis problem is unrealizable (i.e., has no solution in a given search space of programs). Prior work on unrealizability has developed some automatic techniques to establish that a problem is unrealizable; however, these techniques are all black-box , meaning that they conceal the reasoning behind why a synthesis problem is unrealizable. In this paper, we present a Hoare-style reasoning system, called unrealizability logic for establishing that a program-synthesis problem is unrealizable. To the best of our knowledge, unrealizability logic is the first proof system for overapproximating the execution of an infinite set of imperative programs. The logic provides a general, logical system for building checkable proofs about unrealizability. Similar to how Hoare logic distills the fundamental concepts behind algorithms and tools to prove the correctness of programs, unrealizability logic distills into a single logical system the fundamental concepts that were hidden within prior tools capable of establishing that a program-synthesis problem is unrealizable. 

Every program should be accompanied by a specification that describes important aspects of the code's behavior, but writing good specifications is often harder than writing the code itself. This paper addresses the problem of synthesizing specifications automatically, guided by user-supplied inputs of two kinds: i) a query posed about a set of function definitions, and ii) a domain-specific language L in which the extracted property is to be expressed (we call properties in the language L-properties). Each of the property is a best L-property for the query: there is no other L-property that is strictly more precise. Furthermore, the set of synthesized L-properties is exhaustive: no more L-properties can be added to it to make the conjunction more precise. We implemented our method in a tool, Spyro. The ability to modify both the query and L provides a Spyro user with ways to customize the kind of specification to be synthesized. We use this ability to show that Spyro can be used in a variety of applications, such as mining program specifications, performing abstract-domain operations, and synthesizing algebraic properties of program modules. 

Many program-analysis problems can be formulated as graph-reachability problems. Interleaved Dyck language reachability ( InterDyck -reachability) is a fundamental framework to express a wide variety of program-analysis problems over edge-labeled graphs. The InterDyck language represents an intersection of multiple matched-parenthesis languages (i.e., Dyck languages). In practice, program analyses typically leverage one Dyck language to achieve context-sensitivity, and other Dyck languages to model data dependencies, such as field-sensitivity and pointer references/dereferences. In the ideal case, an InterDyck -reachability framework should model multiple Dyck languages simultaneously . Unfortunately, precise InterDyck -reachability is undecidable. Any practical solution must over-approximate the exact answer. In the literature, a lot of work has been proposed to over-approximate the InterDyck -reachability formulation. This article offers a new perspective on improving both the precision and the scalability of InterDyck -reachability: we aim at simplifying the underlying input graph G . Our key insight is based on the observation that if an edge is not contributing to any InterDyck -paths, we can safely eliminate it from G . Our technique is orthogonal to the InterDyck -reachability formulation and can serve as a pre-processing step with any over-approximating approach for InterDyck -reachability. We have applied our graph simplification algorithm to pre-processing the graphs from a recent InterDyck -reachability-based taint analysis for Android. Our evaluation of three popular InterDyck -reachability algorithms yields promising results. In particular, our graph-simplification method improves both the scalability and precision of all three InterDyck -reachability algorithms, sometimes dramatically. 

An interleaved-Dyck (InterDyck) language consists of the interleaving of two or more Dyck languages, where each Dyck language represents a set of strings of balanced parentheses.InterDyck-reachability is a fundamental framework for program analyzers that simultaneously track multiple properly-matched pairs of actions such as call/return, lock/unlock, or write-data/read-data.Existing InterDyck-reachability algorithms are based on the well-known tabulation technique. This paper presents a new perspective on solving InterDyck-reachability. Our key observation is that for the single-source-single-target InterDyck-reachability variant, it is feasible to summarize all paths from the source node to the target node based onpath expressions. Therefore, InterDyck-reachability becomes an InterDyck-path-recognition problem over path expressions. Instead of computing summary edges as in traditional tabulation algorithms, this new perspective enables us to express InterDyck-reachability as aparenthesis-countingproblem, which can be naturally formulated via integer linear programming (ILP). We implemented our ILP-based algorithm and performed extensive evaluations based on two client analyses (a reachability analysis for concurrent programs and a taint analysis). In particular, we evaluated our algorithm against two types of algorithms: (1) the general all-pairs InterDyck-reachability algorithms based on linear conjunctive language (LCL) reachability and synchronized pushdown system (SPDS) reachability, and (2) two domain-specific algorithms for both client analyses. The experimental results are encouraging. Our algorithm achieves 1.42×, 28.24×, and 11.76× speedup for the concurrency-analysis benchmarks compared to all-pair LCL-reachability, SPDS-reachability, and domain-specific tools, respectively; 1.2×, 69.9×, and 0.98× speedup for the taint-analysis benchmarks. Moreover, the algorithm also provides precision improvements, particularly for taint analysis, where it achieves 4.55%, 11.1%, and 6.8% improvement, respectively. 

This paper is a tutorial on algebraic program analysis. It explains the foundations of algebraic program analysis, its strengths and limitations, and gives examples of algebraic program analyses for numerical invariant generation and termination analysis.