From Patterns to Maze Structures: SMT-Based Path Synthesis and 2D/3D Construction

Constraint Answer Set Programming (CASP) is a hybrid reasoning paradigm that combines Answer Set Programming (ASP) with Constraint Processing and Satisfiability Modulo Theories (SMT), enabling powerful declarative encodings of complex combinatorial search problems. This paper presents the design and implementation of EZSMTV3, an extensible SMT-based CASP framework that advances the translational approach to CASP solving. Building upon the foundation of the EZSMT+ system, EZSMTV3 introduces a more expressive input language, supports optimization via weak constraints, and offers foundations for streamlined integration of new constraint types. Rather than implementing custom search procedures, EZSMTV3 leverages state-of-the-art SMT solvers, such as CVC5, YICES, and Z3 to perform reasoning. The paper provides benchmarking results comparing EZSMTV3 with its CASP peers such as CLINGCON, CLINGO[DL], and CLINGO[LP], while showcasing its ability to handle mixed-domain constraints involving both integers and reals. The system provides a robust platform for future extensions and theoretical exploration within the CASP domain.

Synthesizing a reactive system from specifications given in linear temporal logic (LTL) is a classical problem, finding its applications in safety-critical systems design. These systems are typically represented using either Mealy machines or AIGER circuits. We present the second version of SemML, which outperforms all state-of-the-art tools for finding either solution. Aside from implementing the classical automata-theoretic approach, our tool utilizes partial exploration and machine-learning guidance for obtaining solutions efficiently, and numerous heuristics and improvements of classic algorithms for extracting small representations of these solutions. We evaluate our tool against the existing state-of-the-art tools (in particular Strix, LtlSynt, and the previous version of SemML) on the dataset of the synthesis competition SYNTCOMP. We show that we solve significantly more instances and do so much faster than other tools, while maintaining state-of-the-art solution quality.

Structure-mapping forms analogies by aligning systems of relationally connected elements based on shared structure instead of surface features. We introduce a new structure-mapping algorithm: Structure-Mapping with Tight Bounds (SMTB) that is 5--15x faster than the structure-mapping engine (SME) and about 50% better at finding mappings in large nested domains. SMTB is part of the broader Cognitive Rule Engine (CRE) project, a flexible multi-language-compatible framework with an accessible Python interface to state-of-the-art C++ implementations of core algorithms commonly used in cognitive systems such as pattern matching, planning, and structure-mapping. CRE and SMTB are designed to work with a wide range of representation choices. Unlike SME, which biases higher-order correspondences in tree-like predicate logic, SMTB maximizes relational connectivity without privileging higher-order relations. This allows SMTB to work just as well over arbitrary relational graphs as it does in tree-like domains of nested predicate logic. We discuss situations where privileging "higher-orderness" in structure-mapping can cause issues, and illustrate how SMTB avoids failure modes that SME would encounter in these situations. We also provide an evaluation comparing SMTB to SME v4 over 5845 domain pairs from the SME corpus.