Related papers: SMT Solving for Functional Programming over Infini…
In this position paper, we present a prototype of a visualizer for functional programs. Such programs, whose evaluation model is the reduction of an expression to a value through repeated application of rewriting rules, and which tend to…
Structured, procedural reasoning is essential for Large Language Models (LLMs), especially in mathematics. While post-training methods have improved LLM performance, they still fall short in capturing deep procedural logic on complex tasks.…
The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…
The semantic foundations for logic programming are usually separated into two different approaches. The operational semantics, which uses SLD-resolution, the proof method that computes answers in logic programming, and the declarative…
We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our…
The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of…
Regular functions from infinite words to infinite words can be equivalently specified by MSO-transducers, streaming $\omega$-string transducers as well as deterministic two-way transducers with look-ahead. In their one-way restriction, the…
The systematic modelling of dynamic spatial systems is a key requirement in a wide range of application areas such as commonsense cognitive robotics, computer-aided architecture design, and dynamic geographic information systems. We present…
In solving a query, the SLD proof procedure for definite programs sometimes searches an infinite space for a non existing solution. For example, querying a planner for an unreachable goal state. Such programs motivate the development of…
This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…
Existing math datasets evaluate the reasoning abilities of large language models (LLMs) by either using the final answer or the intermediate reasoning steps derived from static examples. However, the former approach fails to surface model's…
This paper deals with formulas of set theory which force the infinity. For such formulas, we provide a technique to infer satisfiability from a finite assignment.
We present a tool for verification of deterministic programs with shared mutable references against specifications such as assertions, preconditions, postconditions, and read/write effects. We implement our tool by encoding programs with…
Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…
Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued…
We present a semi-automated framework to construct and reason about programs in a deeply-embedded while-language. The while-language we consider is a simple computation model that can simulate (and be simulated by) Turing Machines with a…
We analyse the complexity of the satisfiability problem ssmSAT for State Space Models (SSM), which asks whether an input sequence can lead the model to an accepting configuration. We find that ssmSAT is undecidable in general, reflecting…
System-Level Test (SLT) has been a part of the test flow for integrated circuits for over a decade and still gains importance. However, no systematic approaches exist for test program generation, especially targeting non-functional…
In this paper, we explore the concept of modularity in first-order answer set programming (ASP). We introduce a new formalism called parametric modular logic programs, which allows defining subprograms with parameters and intensionality…
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…