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We identify a decidable synthesis problem for a class of programs of unbounded size with conditionals and iteration that work over infinite data domains. The programs in our class use uninterpreted functions and relations, and abide by a…
Chain-of-Thought (CoT) has been shown to empirically improve Transformers' performance, and theoretically increase their expressivity to Turing completeness. However, whether Transformers can learn to generalize to CoT traces longer than…
Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. Its worst-case hardness lies at the core of computational complexity theory, for example in the form of NP-hardness and the (Strong) Exponential…
A major challenge for transformers is generalizing to sequences longer than those observed during training. While previous works have empirically shown that transformers can either succeed or fail at length generalization depending on the…
Modern program verifiers use logic-based encodings of the verification problem that are discharged by a back end reasoning engine. However, instances of such encodings for large programs can quickly overwhelm these back end solvers. Hence,…
We discuss the topic of unsatisfiability proofs in SMT, particularly with reference to quantifier free non-linear real arithmetic. We outline how the methods here do not admit trivial proofs and how past formalisation attempts are not…
In the last two decades, modal and description logics have been applied to numerous areas of computer science, including knowledge representation, formal verification, database theory, distributed computing and, more recently, semantic web…
Many real applications problems can be encoded easily as quantified formulas in SMT. However, this simplicity comes at the cost of difficulty during solving by SMT solvers. Different strategies and quantifier instantiation techniques have…
The determinisation problem for min-plus (tropical) weighted automata was recently shown to be decidable. However, the proof is purely existential, relying on several non-constructive arguments. Our contribution in this work is twofold:…
Transformer large language models (LLMs) have sparked admiration for their exceptional performance on tasks that demand intricate multi-step reasoning. Yet, these models simultaneously show failures on surprisingly trivial problems. This…
Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…
Complex reasoning aims to draw a correct inference based on complex rules. As a hallmark of human intelligence, it involves a degree of explicit reading comprehension, interpretation of logical knowledge and complex rule application. In…
We examine verification of concurrent programs under the total store ordering (TSO) semantics used by the x86 architecture. In our model, threads manipulate variables over infinite domains and they can check whether variables are related…
This paper examines the complexity of hybrid logics over transitive frames, transitive trees, and linear frames. We show that satisfiability over transitive frames for the hybrid language extended with the downarrow operator is…
As transformers have gained prominence in natural language processing, some researchers have investigated theoretically what problems they can and cannot solve, by treating problems as formal languages. Exploring such questions can help…
We show that the satisfiability and finite satisfiability problems for the two-variable fragment of first-order logic with counting quantifiers are both in NEXPTIME, even when counting quantifiers are coded succinctly.
The finite satisfiability problem of monadic second order logic is decidable only on classes of structures of bounded tree-width by the classic result of Seese (1991). We prove the following problem is decidable: Input: (i) A monadic second…
Weighted knowledge bases for description logics with typicality under a "concept-wise" multi-preferential semantics provide a logical interpretation of MultiLayer Perceptrons. In this context, Answer Set Programming (ASP) has been shown to…
We revisit evaluation of logical formulas that allow both uninterpreted relations, constrained to be finite, as well as an interpreted vocabulary over an infinite domain. This formalism was denoted embedded finite model theory in the past.…
We determine the complexity of several constraint satisfaction problems using the heuristic algorithm, WalkSAT. At large sizes N, the complexity increases exponentially with N in all cases. Perhaps surprisingly, out of all the models…