Computational Logic and Formal Languages
Summary
Computational logic and formal languages lie at the core of theoretical computer science, unifying the mathematical study of computation with the precise description of symbolic structures. Formal languages are sets of strings over alphabets, classified by the resources required to recognise them—from regular and context-free to recursively enumerable languages in the Chomsky hierarchy. Automata models (finite automata, pushdown automata, Turing machines) characterise expressiveness, closure properties and decision problems. Computational logic provides the tools to specify, reason about and verify systems: propositional and first-order logics underpin specification languages, while higher-order and modal logics capture richer properties. Decision procedures, theorem-proving techniques and model-checking algorithms translate logical specifications into automatons or constraint systems, enabling automated verification of hardware, software and protocols. In recent years this interplay has extended to quantum and probabilistic models, weighted and timed systems, and logics for infinite structures, reflecting the global mission of ensuring correctness and performance in critical applications.
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Computational Logic and Formal Languages publication trend
The graph below shows the total number of articles in computational logic and formal languages across all publications each year (not limited to Nature Index journals).
Technical terms
Finite automaton: An abstract machine with a finite set of states and transitions that accepts or rejects finite input strings.
Regular language: A class of languages recognised by finite automata or described by regular expressions, known for robust closure and decidability properties.
Context-free language: A class of languages generated by context-free grammars and recognised by pushdown automata, suitable for nested or recursive structures.
Partial-derivative transducer: A device that, given a regular expression, constructs an automaton mapping input strings to outputs via derivative operations extended to two alphabets.
Jumping automaton: A variant of ω-automaton that processes infinite words by non-consecutive symbol selection under specified permutation constraints.
Quantum finite automaton: A finite-state machine augmented with quantum superposition and measurement, yielding probabilistic acceptance with potential state succinctness advantages.
References
- Unary Quantum Finite State Automata with Control Language. Applied Sciences (2024).
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