Lecture Notes on Monadic First- and Second-Order Logic on Strings

2023/01/25 by Dino Mandrioli, Mandrioli, Dino, Davide Martinenghi +7
Computer Science · #Algorithms and Data Compression #F.4.1 #F.4.3 #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Natural Language Processing Techniques #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2301.10519

openalex publication_date 2023/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

These notes present the essentials of first- and second-order monadic logics on strings with introductory purposes. We discuss Monadic First-Order logic and show that it is strictly less expressive than Finite-State Automata, in that it only captures a strict subset of Regular Languages -- the non-counting ones. We then introduce Monadic Second-Order logic; such a logic is, syntactically, a superset of Monadic First-Order logic and captures Regular Languages exactly. We also show how to transform an automaton into a corresponding formula and vice versa. Finally, we discuss the use of logical characterizations of classes of languages as the basis for automatic verification techniques.

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