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Chain-of-Thought (CoT) reasoning enhances Large Language Models (LLMs) by prompting intermediate steps, improving accuracy and robustness in arithmetic, logic, and commonsense tasks. However, this benefit comes with high computational…

Determining whether a program terminates is a central problem in computer science. Turing's Halting Problem established termination as undecidable, showing that no algorithm can universally determine termination for all programs and inputs.…

While loops are present in virtually all imperative programming languages. They are important both for practical reasons (performing a number of iterations not known in advance) and theoretical reasons (achieving Turing completeness). In…

Numerical software are widely used in safety-critical systems such as aircrafts, satellites, car engines and so on, facilitating dynamics control of such systems in real time, it is therefore absolutely necessary to verify their…

Large language models (LLMs) can perform complex reasoning in few- and zero-shot settings by generating intermediate chain of thought (CoT) reasoning steps. Further, each reasoning step can rely on external tools to support computation…

This paper presents a proof system for reasoning about execution time bounds for a core imperative programming language. Proof systems are defined for three different scenarios: approximations of the worst-case execution time, exact time…

Large Reasoning Models (LRMs) achieve impressive performance on complex reasoning tasks via Chain-of-Thought (CoT) reasoning, which enables them to generate intermediate thinking tokens before arriving at the final answer. However, LRMs…

Linear Time Invariant (LTI) systems are ubiquitous in control applications. Unbounded-time reachability analysis that can cope with industrial-scale models with thousands of variables is needed. To tackle this problem, we use abstract…

This paper presents a MATLAB toolbox for implementing robust-to-early termination model predictive control, abbreviated as REAP, which is designed to ensure a sub-optimal yet feasible solution when MPC computations are prematurely…

We present an approach to parameterized reachability for communicating finite-state threads that formulates the analysis as a satisfiability problem. In addition to the unbounded number of threads, the main challenge for SAT/SMT-based…

The field of fine-grained complexity aims at proving conditional lower bounds on the time complexity of computational problems. One of the most popular assumptions, Strong Exponential Time Hypothesis (SETH), implies that SAT cannot be…

Satisfiability checking for Linear Temporal Logic (LTL) is a fundamental step in checking for possible errors in LTL assertions. Extant LTL satisfiability checkers use a variety of different search procedures. With the sole exception of LTL…

While there are many approaches for automatically proving termination of term rewrite systems, up to now there exist only few techniques to disprove their termination automatically. Almost all of these techniques try to find loops, where…

We consider the problem of automatically proving resource bounds. That is, we study how to prove that an integer-valued resource variable is bounded by a given program expression. Automatic resource-bound analysis has recently received…

As demand for Real-Time applications rises among the general public, the importance of enabling large-scale, unbound algorithms to solve conventional problems with low to no latency is critical for product viability. Timer algorithms are…

On the one hand, termination analysis of logic programs is now a fairly established research topic within the logic programming community. On the other hand, non-termination analysis seems to remain a much less attractive subject. If we…

The success of large-scale language models like GPT can be attributed to their ability to efficiently predict the next token in a sequence. However, these models rely on constant computational effort regardless of the complexity of the…

On one hand, termination analysis of logic programs is now a fairly established research topic within the logic programming community. On the other hand, non-termination analysis seems to remain a much less attractive subject. If we divide…

We present here a new explicit reasoning framework for linear temporal logic (LTL), which is built on top of propositional satisfiability (SAT) solving. As a proof-of-concept of this framework, we describe a new LTL satisfiability tool,…

The general setting of this work is the constraint-based synthesis of termination arguments. We consider a restricted class of programs called lasso programs. The termination argument for a lasso program is a pair of a ranking function and…