We characterize provability in intuitionistic logic with equality in terms of a constraint calculus. This characterization uncovers close connections between provability in intuitionistic logic with equality and solutions to simultaneous rigid E-uniication. We show that the problem of existence of a sequent proof with a given skeleton is polynomial-time equivalent to simultaneous rigid E-uniiab...

We extend dynamic logic of propositional assignments by adding an operator parallel composition that is inspired separation logics. provide axiomatization via reduction axioms, thereby establishing decidability. also prove the complexity both model checking and satisfiability problem stay in PSPACE.