Related papers: Partial Redundancy in Saturation
A knowledge base is redundant if it contains parts that can be inferred from the rest of it. We study the problem of checking whether a CNF formula (a set of clauses) is redundant, that is, it contains clauses that can be derived from the…
We present an automated reasoning framework for synthesizing recursion-free programs using saturation-based theorem proving. Given a functional specification encoded as a first-order logical formula, we use a first-order theorem prover to…
The application of automatic transformation processes during the formal development and optimization of programs can introduce encumbrances in the generated code that programmers usually (or presumably) do not write. An example is the…
The problem of detecting and removing redundant constraints is fundamental in optimization. We focus on the case of linear programs (LPs) in dictionary form, given by $n$ equality constraints in $n+d$ variables, where the variables are…
The trapping redundancy of a linear code is the number of rows of a smallest parity-check matrix such that no submatrix forms an $(a,b)$-trapping set. This concept was first introduced in the context of low-density parity-check (LDPC) codes…
Recent large language models have shown promising capabilities in long-form reasoning, following structured chains of thought before arriving at a final answer. However, we observe that these reasoning paths tend to include substantial…
Redundancy identification is an important step of the design flow that typically follows logic synthesis and optimization. In addition to reducing circuit area, power consumption, and delay, redundancy removal also improves testability. All…
We introduce refutationally complete superposition calculi for intentional and extensional clausal $\lambda$-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a…
Redundancy elimination is a key optimization direction, and loop nests are the main optimization target in modern compilers. Previous work on redundancy elimination of array computations in loop nests lacks universality. These approaches…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
Reasoning-capable large language models solve hard problems by emitting long chains of thought, paying heavily in latency, GPU time, and energy. Casual inspection of their traces reveals extensive reformulation, verification, and circular…
Sparse representation over redundant dictionaries constitutes a good model for many classes of signals (e.g., patches of natural images, segments of speech signals, etc.). However, despite its popularity, very little is known about the…
An abstract framework of canonical inference is used to explore how different proof orderings induce different variants of saturation and completeness. Notions like completion, paramodulation, saturation, redundancy elimination, and…
We study the termination problem for nondeterministic recursive probabilistic programs. First, we show that a ranking-supermartingales-based approach is both sound and complete for bounded terminiation (i.e., bounded expected termination…
Multi-threaded programs have many applications which are widely used such as operating systems. Analyzing multi-threaded programs differs from sequential ones; the main feature is that many threads execute at the same time. The effect of…
LLM-based agents have demonstrated strong capabilities in solving complex tasks through multi-step reasoning and tool use. However, existing evaluation protocols primarily focus on task success, overlooking a critical aspect of agent…
We present in this paper a new procedure to saturate a set of clauses with respect to a well-founded ordering on ground atoms such that A < B implies Var(A) {\subseteq} Var(B) for every atoms A and B. This condition is satisfied by any atom…
Transformer-based deep NLP models are trained using hundreds of millions of parameters, limiting their applicability in computationally constrained environments. In this paper, we study the cause of these limitations by defining a notion of…
The task of inferring logical formulas from examples has garnered significant attention as a means to assist engineers in creating formal specifications used in the design, synthesis, and verification of computing systems. Among various…
Trustworthy AI requires reasoning systems that are not only powerful but also transparent and reliable. Automated Theorem Proving (ATP) is central to formal reasoning, yet classical binary resolution remains limited, as each step involves…